A280071 Indices of 11-gonal numbers (A051682) that are also centered 11-gonal numbers (A060544).
1, 12, 232, 4621, 92181, 1838992, 36687652, 731914041, 14601593161, 291299949172, 5811397390272, 115936647856261, 2312921559734941, 46142494546842552, 920536969377116092, 18364596892995479281, 366371400890532469521, 7309063420917653911132
Offset: 1
Examples
12 is in the sequence because the 12th 11-gonal number is 606, which is also the 11th centered 11-gonal number.
Links
- Colin Barker, Table of n, a(n) for n = 1..750
- Index entries for linear recurrences with constant coefficients, signature (21,-21,1).
Programs
-
Mathematica
LinearRecurrence[{21,-21,1},{1,12,232},20] (* Harvey P. Dale, May 27 2025 *) -
PARI
Vec(x*(1 - 9*x + x^2) / ((1 - x)*(1 - 20*x + x^2)) + O(x^30))
Formula
a(n) = (14 + (11-3*sqrt(11))*(10+3*sqrt(11))^n + (10+3*sqrt(11))^(-n)*(11+3*sqrt(11)))/36.
a(n) = 21*a(n-1) - 21*a(n-2) + a(n-3) for n>3.
G.f.: x*(1 - 9*x + x^2) / ((1 - x)*(1 - 20*x + x^2)).
Comments