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 A254626 #16 Jun 15 2024 16:27:05
%S A254626 1,3,23,61,421,1103,7563,19801,135721,355323,2435423,6376021,43701901,
%T A254626 114413063,784198803,2053059121,14071876561,36840651123,252509579303,
%U A254626 661078661101,4531100550901,11862575248703,81307300336923,212865275815561,1459000305513721
%N A254626 Indices of triangular numbers (A000217) that are also centered pentagonal numbers (A005891).
%C A254626 Also positive integers x in the solutions to x^2 - 5*y^2 + x + 5*y - 2 = 0, the corresponding values of y being A254627.
%H A254626 Colin Barker, <a href="/A254626/b254626.txt">Table of n, a(n) for n = 1..1000</a>
%H A254626 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,18,-18,-1,1).
%F A254626 a(n) = a(n-1) + 18*a(n-2) - 18*a(n-3) - a(n-4) + a(n-5).
%F A254626 G.f.: -x*(x+1)^2*(x^2+1) / ((x-1)*(x^2-4*x-1)*(x^2+4*x-1)).
%F A254626 a(n) = (-2 + (2-r)^n - (-2-r)^n*(-2+r) + 2*(-2+r)^n + r*(-2+r)^n + (2+r)^n)/4 where r = sqrt(5). - _Colin Barker_, Nov 25 2016
%e A254626 3 is in the sequence because the 3rd triangular number is 6, which is also the 2nd centered pentagonal number.
%t A254626 LinearRecurrence[{1,18,-18,-1,1},{1,3,23,61,421},30] (* _Harvey P. Dale_, Jun 15 2024 *)
%o A254626 (PARI) Vec(-x*(x+1)^2*(x^2+1)/((x-1)*(x^2-4*x-1)*(x^2+4*x-1)) + O(x^100))
%Y A254626 Cf. A000217, A005891, A254627, A254628.
%K A254626 nonn,easy
%O A254626 1,2
%A A254626 _Colin Barker_, Feb 03 2015