OpenLLM-France/wikimedia huggingface dataset:
# Sequence ValerianDrop

| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 1 | 1 | 3 | 11 | 45 | 203 | 961 | 4565 |

### layer sums of hyperpyramid SyringaDrop

c:Category:Number hyperpyramid SyringaDrop
row sums of JuniperDrop :
🌊    triangle Juniper    row sums Valerian :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 1 | 1 | | | | | | | 2 |
| 2 | 1 | 3 | 1 | | | | | | 5 |
| 3 | 1 | 7 | 7 | 1 | | | | | 16 |
| 4 | 1 | 15 | 29 | 15 | 1 | | | | 61 |
| 5 | 1 | 31 | 100 | 100 | 31 | 1 | | | 264 |
| 6 | 1 | 63 | 306 | 485 | 306 | 63 | 1 | | 1225 |
| 7 | 1 | 127 | 861 | 1906 | 1906 | 861 | 127 | 1 | 5790 |
💧    triangle JuniperDrop    row sums ValerianDrop :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 0 | 1 | | | | | | | 1 |
| 2 | 0 | 2 | 1 | | | | | | 3 |
| 3 | 0 | 4 | 6 | 1 | | | | | 11 |
| 4 | 0 | 8 | 22 | 14 | 1 | | | | 45 |
| 5 | 0 | 16 | 71 | 85 | 30 | 1 | | | 203 |
| 6 | 0 | 32 | 206 | 385 | 275 | 62 | 1 | | 961 |
| 7 | 0 | 64 | 555 | 1421 | 1600 | 798 | 126 | 1 | 4565 |
row sums of SloeDrop :
🌊    triangle Sloe    row sums Valerian :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 · 1 1 | | | | | | | | 1 |
| 1 | 1 · 1 1 | 1 · 1 1 | | | | | | | 2 |
| 2 | 1 · 1 1 | 2 · 1 2 | 1 · 2 2 | | | | | | 5 |
| 3 | 1 · 1 1 | 3 · 1 3 | 3 · 2 6 | 1 · 6 6 | | | | | 16 |
| 4 | 1 · 1 1 | 4 · 1 4 | 6 · 2 12 | 4 · 6 24 | 1 · 20 20 | | | | 61 |
| 5 | 1 · 1 1 | 5 · 1 5 | 10 · 2 20 | 10 · 6 60 | 5 · 20 100 | 1 · 78 78 | | | 264 |
| 6 | 1 · 1 1 | 6 · 1 6 | 15 · 2 30 | 20 · 6 120 | 15 · 20 300 | 6 · 78 468 | 1 · 300 300 | | 1225 |
| 7 | 1 · 1 1 | 7 · 1 7 | 21 · 2 42 | 35 · 6 210 | 35 · 20 700 | 21 · 78 1638 | 7 · 300 2100 | 1 · 1092 1092 | 5790 |
💧    triangle SloeDrop    row sums ValerianDrop :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 · 1 1 | | | | | | | | 1 |
| 1 | 0 | 1 · 1 1 | | | | | | | 1 |
| 2 | 0 | 1 · 1 1 | 1 · 2 2 | | | | | | 3 |
| 3 | 0 | 1 · 1 1 | 2 · 2 4 | 1 · 6 6 | | | | | 11 |
| 4 | 0 | 1 · 1 1 | 3 · 2 6 | 3 · 6 18 | 1 · 20 20 | | | | 45 |
| 5 | 0 | 1 · 1 1 | 4 · 2 8 | 6 · 6 36 | 4 · 20 80 | 1 · 78 78 | | | 203 |
| 6 | 0 | 1 · 1 1 | 5 · 2 10 | 10 · 6 60 | 10 · 20 200 | 5 · 78 390 | 1 · 300 300 | | 961 |
| 7 | 0 | 1 · 1 1 | 6 · 2 12 | 15 · 6 90 | 20 · 20 400 | 15 · 78 1170 | 6 · 300 1800 | 1 · 1092 1092 | 4565 |
row sums of TurnedSloeDrop :
🌊    triangle TurnedSloe    row sums Valerian :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 1 | 1 | | | | | | | 2 |
| 2 | 2 | 2 | 1 | | | | | | 5 |
| 3 | 6 | 6 | 3 | 1 | | | | | 16 |
| 4 | 20 | 24 | 12 | 4 | 1 | | | | 61 |
| 5 | 78 | 100 | 60 | 20 | 5 | 1 | | | 264 |
| 6 | 300 | 468 | 300 | 120 | 30 | 6 | 1 | | 1225 |
| 7 | 1092 | 2100 | 1638 | 700 | 210 | 42 | 7 | 1 | 5790 |
💧    triangle TurnedSloeDrop    row sums ValerianDrop :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 0 | 1 | | | | | | | 1 |
| 2 | 1 | 1 | 1 | | | | | | 3 |
| 3 | 4 | 4 | 2 | 1 | | | | | 11 |
| 4 | 14 | 18 | 9 | 3 | 1 | | | | 45 |
| 5 | 58 | 76 | 48 | 16 | 4 | 1 | | | 203 |
| 6 | 222 | 368 | 240 | 100 | 25 | 5 | 1 | | 961 |
| 7 | 792 | 1632 | 1338 | 580 | 180 | 36 | 6 | 1 | 4565 |
# Triangle Birch

~A139382
triangle Birch (~A139382)    row sums Aster (A135922) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 0 | 1 | | | | | | | 1 |
| 2 | 0 | 1 | 1 | | | | | | 2 |
| 3 | 0 | 1 | 4 | 1 | | | | | 6 |
| 4 | 0 | 1 | 13 | 11 | 1 | | | | 26 |
| 5 | 0 | 1 | 40 | 90 | 26 | 1 | | | 158 |
| 6 | 0 | 1 | 121 | 670 | 480 | 57 | 1 | | 1330 |
| 7 | 0 | 1 | 364 | 4811 | 7870 | 2247 | 120 | 1 | 15414 |
Birch(n, k) is the number of seals with arity = adicity = valency = n and depth = k.
* T(n,k) = (2^k-1) * T(n-1,k) + T(n-1,k-1)
* second diagonal: Eulerian numbers A000295 a(n) = 2^n - n - 1 (see also A125128, A130103)
* column 2: A003462 a(n) = (3^n - 1)/2
* column 3: A016212 a(n) = (7^(n+2) - 3^(n+3) + 2)/24

## Triangles TwistedBirch$_{(Drop)}$

🌊    triangle TwistedBirch (~A139382)    row sums Aster (A135922) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 1 | 0 | | | | | | | 1 |
| 2 | 1 | 1 | 0 | | | | | | 2 |
| 3 | 1 | 4 | 1 | 0 | | | | | 6 |
| 4 | 1 | 11 | 13 | 1 | 0 | | | | 26 |
| 5 | 1 | 26 | 90 | 40 | 1 | 0 | | | 158 |
| 6 | 1 | 57 | 480 | 670 | 121 | 1 | 0 | | 1330 |
| 7 | 1 | 120 | 2247 | 7870 | 4811 | 364 | 1 | 0 | 15414 |
💧    triangle TwistedBirchDrop    row sums AsterDrop :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 0 | 0 | | | | | | | 0 |
| 2 | 0 | 1 | 0 | | | | | | 1 |
| 3 | 0 | 3 | 1 | 0 | | | | | 4 |
| 4 | 0 | 7 | 12 | 1 | 0 | | | | 20 |
| 5 | 0 | 15 | 77 | 39 | 1 | 0 | | | 132 |
| 6 | 0 | 31 | 390 | 630 | 120 | 1 | 0 | | 1172 |
| 7 | 0 | 63 | 1767 | 7200 | 4690 | 363 | 1 | 0 | 14084 |
TwistedBirch(n, k) is the number of seals with arity n and depth k, whose gravity is 0. TwistedBirchDrop(n, k) is the number of seals with adicity n and depth k, whose gravity is 0.
The third diagonal of TwistedBirchDrop is 0, 3, 12, 39, 120, 363... That seems to be $a(n)={\frac {3^{n}-3}{2}}$ (A029858). The equivalent in TwistedBirch is higher by 1: 1, 4, 13, 40, 121, 364... That seems to be $a(n)={\frac {3^{n}-1}{2}}$ (A003462).
The fourth diagonal in TwistedBirch is 1, 11, 90, 670, 4811... That seems to be A016212.

## Triangle Betula

triangle Betula (A156823) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 1 | 1 | | | | | | | 2 |
| 2 | 1 | 4 | 13 | | | | | | 18 |
| 3 | 1 | 11 | 90 | 670 | | | | | 772 |
| 4 | 1 | 26 | 480 | 7870 | 122861 | | | | 131238 |
| 5 | 1 | 57 | 2247 | 77527 | 2526198 | 80189094 | | | 82795124 |
| 6 | 1 | 120 | 9807 | 695368 | 46334382 | 2999255160 | 191467330714 | | 194513625552 |
| 7 | 1 | 247 | 41176 | 5924720 | 798773822 | 104443530554 | 13455795711072 | 1721026866650520 | 1734587910632112 |
Betula is a square array, whose rows are the columns of Birch, but without the empty fields above the diagonal. The rows are then shortened to get a triangle. (This seems like an arbitrary choice, so the row sums probably do not count anything.)
# Triangle Elder
## Triangles Elder$_{(Drop)}$

In the positive columns the diagonals of ElderDrop are entries of Heather. Apart form ElderDrop(0, 0) = 0 the entries in column 0 are the diagonal value minus 1.
🌊    triangle Elder    row sums Basil :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 1 | 1 | | | | | | | 2 |
| 2 | 2 | 2 | 1 | | | | | | 5 |
| 3 | 5 | 4 | 2 | 1 | | | | | 12 |
| 4 | 12 | 8 | 4 | 2 | 1 | | | | 27 |
| 5 | 27 | 16 | 8 | 4 | 2 | 1 | | | 58 |
| 6 | 62 | 32 | 16 | 8 | 4 | 2 | 1 | | 125 |
| 7 | 141 | 68 | 32 | 16 | 8 | 4 | 2 | 1 | 272 |
💧    triangle ElderDrop    row sums MaimedClover :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 0 | 1 | | | | | | | 1 |
| 2 | 1 | 1 | 1 | | | | | | 3 |
| 3 | 3 | 2 | 1 | 1 | | | | | 7 |
| 4 | 7 | 4 | 2 | 1 | 1 | | | | 15 |
| 5 | 15 | 8 | 4 | 2 | 1 | 1 | | | 31 |
| 6 | 35 | 16 | 8 | 4 | 2 | 1 | 1 | | 67 |
| 7 | 79 | 36 | 16 | 8 | 4 | 2 | 1 | 1 | 147 |
# Triangle Juniper
## Triangles Juniper$_{(Drop)}$

🌊    triangle Juniper    row sums Valerian :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 1 | 1 | | | | | | | 2 |
| 2 | 1 | 3 | 1 | | | | | | 5 |
| 3 | 1 | 7 | 7 | 1 | | | | | 16 |
| 4 | 1 | 15 | 29 | 15 | 1 | | | | 61 |
| 5 | 1 | 31 | 100 | 100 | 31 | 1 | | | 264 |
| 6 | 1 | 63 | 306 | 485 | 306 | 63 | 1 | | 1225 |
| 7 | 1 | 127 | 861 | 1906 | 1906 | 861 | 127 | 1 | 5790 |
💧    triangle JuniperDrop    row sums ValerianDrop :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 0 | 1 | | | | | | | 1 |
| 2 | 0 | 2 | 1 | | | | | | 3 |
| 3 | 0 | 4 | 6 | 1 | | | | | 11 |
| 4 | 0 | 8 | 22 | 14 | 1 | | | | 45 |
| 5 | 0 | 16 | 71 | 85 | 30 | 1 | | | 203 |
| 6 | 0 | 32 | 206 | 385 | 275 | 62 | 1 | | 961 |
| 7 | 0 | 64 | 555 | 1421 | 1600 | 798 | 126 | 1 | 4565 |
# Triangle Maple

🌊    triangle Oak (A022166)    row sums Daisy (A006116) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 1 | 1 | | | | | | | 2 |
| 2 | 1 | 3 | 1 | | | | | | 5 |
| 3 | 1 | 7 | 7 | 1 | | | | | 16 |
| 4 | 1 | 15 | 35 | 15 | 1 | | | | 67 |
| 5 | 1 | 31 | 155 | 155 | 31 | 1 | | | 374 |
| 6 | 1 | 63 | 651 | 1395 | 651 | 63 | 1 | | 2825 |
| 7 | 1 | 127 | 2667 | 11811 | 11811 | 2667 | 127 | 1 | 29212 |
💧    triangle Maple (~A289537)    row sums Dahlia (~A182176) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 0 | 1 | | | | | | | 1 |
| 2 | 0 | 2 | 1 | | | | | | 3 |
| 3 | 0 | 4 | 6 | 1 | | | | | 11 |
| 4 | 0 | 8 | 28 | 14 | 1 | | | | 51 |
| 5 | 0 | 16 | 120 | 140 | 30 | 1 | | | 307 |
| 6 | 0 | 32 | 496 | 1240 | 620 | 62 | 1 | | 2451 |
| 7 | 0 | 64 | 2016 | 10416 | 11160 | 2604 | 126 | 1 | 26387 |
Maple(n, k) is the number of seals with adicity n and depth k.

## Triangle MapleCore

* Triangle Oak with multiplied columns
🌊    triangle MapleCore (~A289537)    row sums DahliaCore (A182176) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 · 1 1 | | | | | | | | 1 |
| 1 | 1 · 1 1 | 1 · 2 2 | | | | | | | 3 |
| 2 | 1 · 1 1 | 3 · 2 6 | 1 · 4 4 | | | | | | 11 |
| 3 | 1 · 1 1 | 7 · 2 14 | 7 · 4 28 | 1 · 8 8 | | | | | 51 |
| 4 | 1 · 1 1 | 15 · 2 30 | 35 · 4 140 | 15 · 8 120 | 1 · 16 16 | | | | 307 |
| 5 | 1 · 1 1 | 31 · 2 62 | 155 · 4 620 | 155 · 8 1240 | 31 · 16 496 | 1 · 32 32 | | | 2451 |
| 6 | 1 · 1 1 | 63 · 2 126 | 651 · 4 2604 | 1395 · 8 11160 | 651 · 16 10416 | 63 · 32 2016 | 1 · 64 64 | | 26387 |
| 7 | 1 · 1 1 | 127 · 2 254 | 2667 · 4 10668 | 11811 · 8 94488 | 11811 · 16 188976 | 2667 · 32 85344 | 127 · 64 8128 | 1 · 128 128 | 387987 |
💧    triangle Sycamore    row sums Azalea :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 · 1 1 | | | | | | | | 1 |
| 1 | 0 | 1 · 2 2 | | | | | | | 2 |
| 2 | 0 | 2 · 2 4 | 1 · 4 4 | | | | | | 8 |
| 3 | 0 | 4 · 2 8 | 6 · 4 24 | 1 · 8 8 | | | | | 40 |
| 4 | 0 | 8 · 2 16 | 28 · 4 112 | 14 · 8 112 | 1 · 16 16 | | | | 256 |
| 5 | 0 | 16 · 2 32 | 120 · 4 480 | 140 · 8 1120 | 30 · 16 480 | 1 · 32 32 | | | 2144 |
| 6 | 0 | 32 · 2 64 | 496 · 4 1984 | 1240 · 8 9920 | 620 · 16 9920 | 62 · 32 1984 | 1 · 64 64 | | 23936 |
| 7 | 0 | 64 · 2 128 | 2016 · 4 8064 | 10416 · 8 83328 | 11160 · 16 178560 | 2604 · 32 83328 | 126 · 64 8064 | 1 · 128 128 | 361600 |
MapleCore(n, k) is the number of blocks with arity n and depth k.

## illustrated examples

Oak, Maple (seals with arity 5)       MapleCore, Sycamore (blocks with adicity 4) :
triangles :
# Triangle Oak

A022166
🌊    triangle Oak (A022166)    row sums Daisy (A006116) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 1 | 1 | | | | | | | 2 |
| 2 | 1 | 3 | 1 | | | | | | 5 |
| 3 | 1 | 7 | 7 | 1 | | | | | 16 |
| 4 | 1 | 15 | 35 | 15 | 1 | | | | 67 |
| 5 | 1 | 31 | 155 | 155 | 31 | 1 | | | 374 |
| 6 | 1 | 63 | 651 | 1395 | 651 | 63 | 1 | | 2825 |
| 7 | 1 | 127 | 2667 | 11811 | 11811 | 2667 | 127 | 1 | 29212 |
💧    triangle Maple (~A289537)    row sums Dahlia (~A182176) :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 0 | 1 | | | | | | | 1 |
| 2 | 0 | 2 | 1 | | | | | | 3 |
| 3 | 0 | 4 | 6 | 1 | | | | | 11 |
| 4 | 0 | 8 | 28 | 14 | 1 | | | | 51 |
| 5 | 0 | 16 | 120 | 140 | 30 | 1 | | | 307 |
| 6 | 0 | 32 | 496 | 1240 | 620 | 62 | 1 | | 2451 |
| 7 | 0 | 64 | 2016 | 10416 | 11160 | 2604 | 126 | 1 | 26387 |
Oak(n, k) is the number of seals with arity n and depth k.
This triangle is the basis of many others. See Triangle Oak with multiplied columns.
# Triangle Rowan
## Triangles Rowan$_{(Drop)}$

RowanDrop(n, k) is almost the same as Heather(k), but the first entry in every positive row is 0 instead of 1.
So the entries of Rowan are entries of Heather multiplied by a factor: For positive k: Rowan(n, k) = Heather(k) · (n − k + 1)  E.g. Rowan(6, 4) = Heather(4) · (6 − 4 + 1) = 8 · 3 = 24.
🌊    triangle Rowan    row sums Basil :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 1 | 1 | | | | | | | 2 |
| 2 | 1 | 2 | 2 | | | | | | 5 |
| 3 | 1 | 3 | 4 | 4 | | | | | 12 |
| 4 | 1 | 4 | 6 | 8 | 8 | | | | 27 |
| 5 | 1 | 5 | 8 | 12 | 16 | 16 | | | 58 |
| 6 | 1 | 6 | 10 | 16 | 24 | 32 | 36 | | 125 |
| 7 | 1 | 7 | 12 | 20 | 32 | 48 | 72 | 80 | 272 |
💧    triangle RowanDrop    row sums MaimedClover :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 0 | 1 | | | | | | | 1 |
| 2 | 0 | 1 | 2 | | | | | | 3 |
| 3 | 0 | 1 | 2 | 4 | | | | | 7 |
| 4 | 0 | 1 | 2 | 4 | 8 | | | | 15 |
| 5 | 0 | 1 | 2 | 4 | 8 | 16 | | | 31 |
| 6 | 0 | 1 | 2 | 4 | 8 | 16 | 36 | | 67 |
| 7 | 0 | 1 | 2 | 4 | 8 | 16 | 36 | 80 | 147 |
# Triangle Sloe

* Pascal's triangle with multiplied columns
Compare triangle Ash.

## Triangles Sloe$_{(Drop)}$

The diagonal of both triangles is Verbena.
🌊    triangle Sloe    row sums Valerian :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 · 1 1 | | | | | | | | 1 |
| 1 | 1 · 1 1 | 1 · 1 1 | | | | | | | 2 |
| 2 | 1 · 1 1 | 2 · 1 2 | 1 · 2 2 | | | | | | 5 |
| 3 | 1 · 1 1 | 3 · 1 3 | 3 · 2 6 | 1 · 6 6 | | | | | 16 |
| 4 | 1 · 1 1 | 4 · 1 4 | 6 · 2 12 | 4 · 6 24 | 1 · 20 20 | | | | 61 |
| 5 | 1 · 1 1 | 5 · 1 5 | 10 · 2 20 | 10 · 6 60 | 5 · 20 100 | 1 · 78 78 | | | 264 |
| 6 | 1 · 1 1 | 6 · 1 6 | 15 · 2 30 | 20 · 6 120 | 15 · 20 300 | 6 · 78 468 | 1 · 300 300 | | 1225 |
| 7 | 1 · 1 1 | 7 · 1 7 | 21 · 2 42 | 35 · 6 210 | 35 · 20 700 | 21 · 78 1638 | 7 · 300 2100 | 1 · 1092 1092 | 5790 |
💧    triangle SloeDrop    row sums ValerianDrop :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 · 1 1 | | | | | | | | 1 |
| 1 | 0 | 1 · 1 1 | | | | | | | 1 |
| 2 | 0 | 1 · 1 1 | 1 · 2 2 | | | | | | 3 |
| 3 | 0 | 1 · 1 1 | 2 · 2 4 | 1 · 6 6 | | | | | 11 |
| 4 | 0 | 1 · 1 1 | 3 · 2 6 | 3 · 6 18 | 1 · 20 20 | | | | 45 |
| 5 | 0 | 1 · 1 1 | 4 · 2 8 | 6 · 6 36 | 4 · 20 80 | 1 · 78 78 | | | 203 |
| 6 | 0 | 1 · 1 1 | 5 · 2 10 | 10 · 6 60 | 10 · 20 200 | 5 · 78 390 | 1 · 300 300 | | 961 |
| 7 | 0 | 1 · 1 1 | 6 · 2 12 | 15 · 6 90 | 20 · 20 400 | 15 · 78 1170 | 6 · 300 1800 | 1 · 1092 1092 | 4565 |

## Triangles TurnedSloe$_{(Drop)}$

🌊    triangle TurnedSloe    row sums Valerian :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 1 | 1 | | | | | | | 2 |
| 2 | 2 | 2 | 1 | | | | | | 5 |
| 3 | 6 | 6 | 3 | 1 | | | | | 16 |
| 4 | 20 | 24 | 12 | 4 | 1 | | | | 61 |
| 5 | 78 | 100 | 60 | 20 | 5 | 1 | | | 264 |
| 6 | 300 | 468 | 300 | 120 | 30 | 6 | 1 | | 1225 |
| 7 | 1092 | 2100 | 1638 | 700 | 210 | 42 | 7 | 1 | 5790 |
💧    triangle TurnedSloeDrop    row sums ValerianDrop :
| kn | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | sums |
| 0 | 1 | | | | | | | | 1 |
| 1 | 0 | 1 | | | | | | | 1 |
| 2 | 1 | 1 | 1 | | | | | | 3 |
| 3 | 4 | 4 | 2 | 1 | | | | | 11 |
| 4 | 14 | 18 | 9 | 3 | 1 | | | | 45 |
| 5 | 58 | 76 | 48 | 16 | 4 | 1 | | | 203 |
| 6 | 222 | 368 | 240 | 100 | 25 | 5 | 1 | | 961 |
| 7 | 792 | 1632 | 1338 | 580 | 180 | 36 | 6 | 1 | 4565 |
The left columns are Verbena$_{(Drop)}$.
The first diagonals of TurnedSloeDrop are ones, natural numbers, square numbers, cubic minus square numbers (A045991). (Same as in Alder.)
# WikiJournal User Group

WikiJournal User Group Open access • Publication charge free • Public peer review • Wikipedia-integrated
WikiJournal of Science
WikiJournal of Humanities
WikiJournal of PPB
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WikiJournal User Group is a publishing group of open-access, free-to-publish, Wikipedia-integrated academic journals. <seo title=" Wikiversity Journal User Group, WikiJournal Free to publish, Open access, Open-access, Non-profit, online journal, Public peer review "/>
The WikiJournal User Group publishes a set of open-access, peer-reviewed academic journals with no publishing costs to authors. Its goal is to provide free, quality-assured knowledge. Secondly, it aims to bridge the Academia-Wikipedia gap by enabling expert contributions in the traditional academic publishing format to improve Wikipedia content.
Medicine and biomedicine
Science, mathematics, engineering and technology
Humanities, arts and social sciences
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Content under peer review or still being drafted
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### Discussion forums

Discussion of the projects is encouraged. The forum for the publishing group is here, and each journal has its own additional discussion page.
The journal group is also currently applying to be a Wikimedia Foundation Sister Project. This would give greater control over the workings and formatting of the site, as well as a dedicated domain name.
# Music Form and Analysis

Musical form relates to the structure of a given piece, its themes and the relationship between each theme. There are many varieties of form used in music, both popular and classical.

## Popular Song Form

Most popular music follows the basic structure of Verse-Chorus-Verse-Chorus-Bridge-Chorus. Artists often vary and elaborate on this basic structure.

### Verses and Choruses

Most popular music is shaped around verses and choruses. Each verse has different words [and sometimes different melody and harmonies as well] while the chorus [generally] remains constant. Forms include VVCVCVC… [V-verse C-chorus], CVCV… CC, and variations thereof.

### Bridges

The bridge, at its most basic, is used in songs to provide contrast. Artists often introduce new musical or thematic elements in the bridge before returning to the familiar chorus.

## Binary

In binary music, there are just two different themes which appear only once, one after the other like this:
AB

## Ternary

Ternary music has two themes, one of which appears twice, like this:
ABA

## Rondo

A rondo [rondeau] works as bit like the Verse Chorus form of popular music today. It is also called Ritornello.
ABACADA

## Canon

A canon has a repeated melody line which starts at the same pitch, where each entry is delayed by a few notes. A canon must work so that the harmonies match.

## See Also

* Wikipedia: Musical Form
* Grasping the Whole Composition cnx.org
* ↑ Hutchinson, Robert. Verse-Chorus Form (in en-US). https://musictheory.pugetsound.edu/mt21c/VerseChorusForm.html.
* ↑ "Music Crash Courses". www.musiccrashcourses.com. Retrieved 2025-03-09.
* ↑ Gateway, Music (2019-08-22). "What Is A Pop Song Structure?". Music Gateway. Retrieved 2025-03-09.
* ↑ "What Is a Bridge in a Song and How to Use It". www.iconcollective.edu. 2020-03-11. Retrieved 2025-03-09.
* ↑ Staff, Billboard (2021-05-13). "The 100 Greatest Song Bridges of the 21st Century: Staff Picks". Billboard. Retrieved 2025-03-09.
* ↑ Needs revising; does not consider simple, rounded, continuous, or sectional binary designs.
* ↑ Rewrite; Ritornello is episode-based and typically used for fugue design.
# Concert Percussion

Welcome to the Wikiversity page for Concert Percussion! This page will focus on common unpitched percussion instruments found in concert bands and orchestras, and how to play them. Additionally, famous etudes, excerpts, and solos will be provided for each instrument.
See Mallet instruments for information on how to play mallet percussion instruments.

## The Instruments

As a percussionist in a concert band or orchestra, it's important to have knowledge of multiple instruments as the director or conductor will assign each percussionist to a specific instrument in the piece. The following list contains some of the most frequently used concert percussion instruments in a concert setting:
* Snare drum
* Bass drum
* Crash Cymbals (Piatti)
* Suspended Cymbal
* Tambourine
* Triangle
* Tam-tam (Gong)
* Woodblock
* Latin Percussion
* Other small auxiliary instruments
While these are the most common instruments, many pieces may ask for other auxiliary instruments like different cymbal types, different drums, and more. The techniques of these are otherwise similar to other instruments listed.

## Getting a Teacher

Although this article might be a jump start into helping those interested in playing percussion learn, the best way to learn percussion is to learn from a private instructor. In fact, learning from a private instructor is the best way to learn any instrument. It's often not too hard to find a percussion instructor, asking around on online forums or from friends who play percussion is a great start. Searching up music institutions is also a good way to find instructors. The staff at music institutions are more than willing to help out any struggling percussionists.

## Snare Drum

A snare drum is a type of drum with thin metal wire called snares running along the bottom of the instrument. It's often found on its own or as part of a drum kit.
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## Bass Drum

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## Cymbals

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## Auxiliary Instruments

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## Latin Percussion

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# Software engineering

Software engineering is a field of computer science, concerned with designing and writing programs for computers.
Today it is mostly done in a team. Software engineering can broadly be split into the following:
* Requirements say what the software should do. Note that the requirements can change over time.
* Software design is usually done on paper. It says what the different components of the software are, and how they interact.
* When the design phase is done, engineers program the software in a phase known as implementation.
* At the end of implementation, engineers test their code to see if its components meet the requirements.
Programming is definitely the blood of almost all software. And just like calculus is to engineering, programming is to software engineering.

## Overview

There are four generic phases in Software Engineering which are Analysis, Design, Coding and Testing.[citation needed]

## Concepts
### Coding

* implement system routines
* construct / traverse data structures
* distil large data sets to single values
* transform one data set to another
* language familiarity
* core libraries
* idioms
* performance issues
* readable, well-written, and efficient code

### Algorithm design and analysis

* complexity analysis
* sorting and hashing, searching
* large amounts of data

### Data structures

* tables
* trees
* graphs
* lists

### Systems design

* feature sets
* interfaces
* class hierarchies
* designing a system under certain constraints
* simplicity and robustness
* trade-offs

### Problem-solving

* collaboration
* classes of NP-complete problems
* listening and comprehension
* asking the right questions
* don't use brute force solutions
* don't assume things
* find multiple solutions and choose the best
* be open to new ideas and ways of solving the problem
* ask questions to move to a more complex answer

### Mathematics

* matrices
* discrete math
* probability
* combinatorics

## Becoming a software engineer

* How to prepare for a software engineering technical interview

## Printed resources

* Laplante, Phillip (2007). What Every Engineer Should Know about Software Engineering. Boca Raton: CRC. ISBN 9780849372285. http://books.google.com/books?id=pFHYk0KWAEgC&lpg=PP1&ots=bqe_WFF-gi&dq=What%20Every%20Engineer%20Should%20Know%20about%20Software%20Engineering.&pg=PA1#v=onepage&q&f=false. Retrieved 2011-01-21.

## Other websites

* The British Computer Society
* The Institution of Electrical and Electronics Engineers
* Computer Degrees and Careers