This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A280071 #10 May 27 2025 18:17:07
%S A280071 1,12,232,4621,92181,1838992,36687652,731914041,14601593161,
%T A280071 291299949172,5811397390272,115936647856261,2312921559734941,
%U A280071 46142494546842552,920536969377116092,18364596892995479281,366371400890532469521,7309063420917653911132
%N A280071 Indices of 11-gonal numbers (A051682) that are also centered 11-gonal numbers (A060544).
%C A280071 Also positive integers x in the solutions to 9*x^2 - 11*y^2 - 7*x + 11*y - 2 = 0, the corresponding values of y being A280072.
%H A280071 Colin Barker, <a href="/A280071/b280071.txt">Table of n, a(n) for n = 1..750</a>
%H A280071 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-21,1).
%F A280071 a(n) = (14 + (11-3*sqrt(11))*(10+3*sqrt(11))^n + (10+3*sqrt(11))^(-n)*(11+3*sqrt(11)))/36.
%F A280071 a(n) = 21*a(n-1) - 21*a(n-2) + a(n-3) for n>3.
%F A280071 G.f.: x*(1 - 9*x + x^2) / ((1 - x)*(1 - 20*x + x^2)).
%e A280071 12 is in the sequence because the 12th 11-gonal number is 606, which is also the 11th centered 11-gonal number.
%t A280071 LinearRecurrence[{21,-21,1},{1,12,232},20] (* _Harvey P. Dale_, May 27 2025 *)
%o A280071 (PARI) Vec(x*(1 - 9*x + x^2) / ((1 - x)*(1 - 20*x + x^2)) + O(x^30))
%Y A280071 Cf. A051682, A060544, A131215, A280072
%K A280071 nonn,easy
%O A280071 1,2
%A A280071 _Colin Barker_, Dec 25 2016