A280072 Indices of centered 11-gonal numbers (A060544) that are also 11-gonal numbers (A051682).
1, 11, 210, 4180, 83381, 1663431, 33185230, 662041160, 13207637961, 263490718051, 5256606723050, 104868643742940, 2092116268135741, 41737456718971871, 832657018111301670, 16611402905507061520, 331395401092029928721, 6611296618935091512891
Offset: 1
Examples
11 is in the sequence because the 11th centered 11-gonal number is 606, which is also the 12th 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
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Mathematica
LinearRecurrence[{21,-21,1},{1,11,210},20] (* Harvey P. Dale, Aug 19 2020 *) -
PARI
Vec(x*(1 - 10*x) / ((1 - x)*(1 - 20*x + x^2)) + O(x^30)) \\ Colin Barker, Dec 25 2016
Formula
a(n) = (6 - (3+sqrt(11))*(10+3*sqrt(11))^(-n) + (-3+sqrt(11))*(10+3*sqrt(11))^n)/12.
a(n) = 21*a(n-1) - 21*a(n-2) + a(n-3) for n>3.
G.f.: x*(1 - 10*x) / ((1 - x)*(1 - 20*x + x^2)).
Comments