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 A254654 #15 Jan 10 2025 18:46:46
%S A254654 1,22,11572,265651,139997551,3213845272,1693690359922,38881099834501,
%T A254654 20490265834338301,470383542583947322,247891234370134405072,
%U A254654 5690700059299494866551,2998988132919620198222251,68846088847021746311586172,36281758184170330787958387022
%N A254654 Pentagonal numbers (A000326) which are also centered heptagonal numbers (A069099).
%H A254654 Colin Barker, <a href="/A254654/b254654.txt">Table of n, a(n) for n = 1..490</a>
%H A254654 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,12098,-12098,-1,1).
%F A254654 a(n) = a(n-1)+12098*a(n-2)-12098*a(n-3)-a(n-4)+a(n-5).
%F A254654 G.f.: -x*(x^4+21*x^3-548*x^2+21*x+1) / ((x-1)*(x^2-110*x+1)*(x^2+110*x+1)).
%e A254654 22 is in the sequence because it is the 4th pentagonal number and the 3rd centered heptagonal number.
%t A254654 CoefficientList[Series[(x^4 + 21*x^3 - 548*x^2 + 21*x + 1)/((1 - x)*(x^2 - 110*x + 1)*(x^2 + 110*x + 1)), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Jan 19 2017 *)
%t A254654 LinearRecurrence[{1,12098,-12098,-1,1},{1,22,11572,265651,139997551},20] (* _Harvey P. Dale_, Jan 10 2025 *)
%o A254654 (PARI) Vec(-x*(x^4+21*x^3-548*x^2+21*x+1)/((x-1)*(x^2-110*x+1)*(x^2+110*x+1)) + O(x^100))
%o A254654 (Magma) I:=[1,22,11572,265651,139997551]; [n le 5 select I[n] else Self(n-1)+12098*Self(n-2)-12098*Self(n-3)-Self(n-4)+Self(n-5): n in [1..20]]; // _Vincenzo Librandi_, Jan 20 2017
%Y A254654 Cf. A000326, A069099, A254652, A254653.
%K A254654 nonn,easy
%O A254654 1,2
%A A254654 _Colin Barker_, Feb 04 2015