# Overview of sequences related to Boolean functions

This page will be a collection of all integer sequences that appear in the project Studies of Boolean functions. They appear in the following articles: Integer sequences related to Boolean functions, Seal (discrete mathematics), Gender of Boolean functions
Templates: general, seal
Boolean functions :
| | | all | dense | ♂ | ♀ | ♂−♀ | self- reverse | self- dual |
| sequences | a | Grass GrassDrop | Lotus LotusDrop | HalfCrocus HalfCrocusDrop | Primula PrimulaDrop | Hyacinth HyacinthDrop | ~Grass ~GrassDrop | ~Grass ~GrassDrop |
| triangles | a, s | Poplar PoplarDrop | | | | | | |
| triangles | a, d | TurnedPoplar TurnedPoplarDrop | | | | | | |
| triangles | a, v | Willow WillowDrop | | HalfCedar HalfCedarDrop | Robinia RobiniaDrop | Hickory HickoryDrop | Chestnut ChestnutDrop | Chinkapin ChinkapinDrop |
| triangles | a, g | TurnedWillow TurnedWillowDrop | | | | | | |
families :
| | | all | blunt | sharp | intro- verted | extro- verted |
| sequences | a | Thyme ThymeDrop | Balm BalmDrop | Sage SageDrop | Mint MintDrop | DubSage DubSageDrop |
| triangles | a, s | Olive OliveDrop | | | | |
| triangles | a, d | | | | | |
| triangles | a, v | | | | | |
| triangles | a, g | | | | | |

## Seals

pairs :
| | | houses | rooms | ? | seals | blocks |
| sequences | a | Clover Heather | Basil MaimedClover | Valerian ValerianDrop | Daisy Dahlia | DahliaCore Azalea |
| triangles | a, d | Elm Lime | Aronia MaimedElm | Juniper JuniperDrop | Oak Maple | MapleCore Sycamore |
| triangles | a, v | | Rowan RowanDrop | Sloe SloeDrop | Ash Aspen | |
| triangles | a, g | | Elder ElderDrop | TurnedSloe TurnedSloeDrop | TwistedAsh Alder | |
| pyramids | a, d, v | | | | Liana Ivy | |
| pyramids | a, d, g | | | | TwistedLiana Lonicera | |
| hyper- pyramids | a, d, v, g | empty | Wisteria WisteriaDrop | Syringa SyringaDrop | Jacaranda JacarandaDrop | |
* Triangle Magnolia appears in hyperpyramid Wisteria, but does not seem to count anything on its own. Its row sums are Lavender.
* Triangle Birch is the number of seals by a=v and d. Its row sums are Aster.
* Triangles TwistedBirch/TwistedBirchDrop are the number of seals with g=0 by a and d. Their row sums are Aster/AsterDrop.
| a | 🌊 arity 💧 adicity |
| d | depth |
| v | valency |
| g | gravity |
Arity n is short for adicity ≤ n. Sequences, triangles and pyramids using arity are marked with a wave 🌊, those using adicity are marked with a drop 💧. 🌊 entries are sums of 💧 columns.
sequences :
| name | OEIS | description | entries |
| Rose | A190939 | truth tables | 1, 3, 5, 9, 15, 17, 33, 51, 65, 85, 105, 129, 153, 165, 195, 255 |
| Tulip | | Zhegalkin indices | 1, 3, 5, 7, 15, 17, 19, 21, 23, 51, 63, 85, 95, 119, 127, 255 |
| LeanMaitake | A305737 | | 1, 2, 8, 184, 62464 |
| | | Betula sums | 1, 2, 18, 772, 131238, 82795124, 194513625552, 1734587910632112 |
| | | Betula diagonal | 1, 1, 13, 670, 122861, 80189094, 191467330714, 1721026866650520 |
| Aster | A135922 | | 1, 1, 2, 6, 26, 158, 1330, 15414 |
| AsterDrop | | | 1, 0, 1, 4, 20, 132, 1172, 14084 |
| Daisy | A006116 | | 1, 2, 5, 16, 67, 374, 2825, 29212 |
| Dahlia | ~A182176 | | 1, 1, 3, 11, 51, 307, 2451, 26387 |
| Clover | A076766 | | 1, 2, 4, 8, 16, 32, 68, 148 |
| Heather | ~A034343 | | 1, 1, 2, 4, 8, 16, 36, 80 |
| DahliaCore | A182176 | | 1, 3, 11, 51, 307, 2451, 26387, 387987 |
| Azalea | | | 1, 2, 8, 40, 256, 2144, 23936, 361600 |
| Valerian | | | 1, 2, 5, 16, 61, 264, 1225, 5790 |
| ValerianDrop | | | 1, 1, 3, 11, 45, 203, 961, 4565 |
| Basil | | | 1, 2, 5, 12, 27, 58, 125, 272 |
| MaimedClover | | | 1, 1, 3, 7, 15, 31, 67, 147 |
| Verbena | | | 1, 1, 2, 6, 20, 78, 300, 1092 |
triangles :
| name | OEIS | description |
| Birch | ~A139382 | |
| Betula | A156823 | part of Birch |
| Oak | A022166 | |
| Maple | ~A289537 | |
| Ash | | |
| Aspen | | |
| TwistedAsh | | |
| Alder | | |
| Elm | A076831 | |
| Lime | ~A034253 | |
| Tilia | ~A076832 | Difference of neighbors gives entry of Lime. |
| MapleCore | ~A289537 | |
| Sycamore | | |
| TwistedBirch | ~A139382 | |
| TwistedBirchDrop | | |