 280px|right a centered decagonal number is a centered figurate number that represents a decagon with a dot in the center and all other dots surrounding the center dot in successive decagonal layers. the centered decagonal number for n is given by the formula :5n^2+5n+1 \, thus, the first few centered decagonal numbers are :1, 11, 31, 61, 101, 151, 211, 281, 361, 451, 551, 661, 781, 911, 1051, ...  like any other centered k-gonal number, the nth centered decagonal number can reckoned by multiplying the (n&nbsp;&minus;&nbsp;1)th triangular number by k, 10 in this case, then adding 1. as a consequence of performing the calculation in base 10, the centered decagonal numbers can be obtained by simply adding a 1 to the right of each triangular number. therefore, all centered decagonal numbers are odd and in base 10 always end in&nbsp;1. another consequence of this relation to triangular numbers is the simple recurrence relation for centered decagonal numbers: :cd_{n+1} = cd_n+10n , where :cd_0 = 0 . ==centered decagonal prime== a centered decagonal prime is a centered decagonal number that is prime. the first few centered decagonal primes are: :11, 31, 61, 101, 151, 211, 281, 661, 911, 1051, 1201, 1361, 1531, 1901, 2311, 2531, 3001, 3251, 3511, 4651, 5281, .... ==see also== *[ordinary] decagonal number 
Figurate_numbers