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 A253921 #12 Sep 08 2022 08:46:11
%S A253921 1,51,271,24421,130461,11770711,62881771,5673458121,30308883001,
%T A253921 2734595043451,14608818724551,1318069137485101,7041420316350421,
%U A253921 635306589672775071,3393949983662178211,306216458153140098961,1635876850704853547121,147595697523223854923971
%N A253921 Indices of octagonal numbers (A000567) which are also centered pentagonal numbers (A005891).
%C A253921 Also positive integers x in the solutions to 6*x^2 - 5*y^2 - 4*x + 5*y - 2 = 0, the corresponding values of y being A253922.
%H A253921 Colin Barker, <a href="/A253921/b253921.txt">Table of n, a(n) for n = 1..745</a>
%H A253921 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,482,-482,-1,1).
%F A253921 a(n) = a(n-1)+482*a(n-2)-482*a(n-3)-a(n-4)+a(n-5).
%F A253921 G.f.: -x*(x^4+50*x^3-262*x^2+50*x+1) / ((x-1)*(x^2-22*x+1)*(x^2+22*x+1)).
%e A253921 51 is in the sequence because the 51st octagonal number is 7701, which is also the 56th centered pentagonal number.
%t A253921 CoefficientList[Series[(x^4 + 50 x^3 - 262 x^2 + 50 x + 1)/((1 - x) (x^2 - 22 x + 1) (x^2 + 22 x + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 20 2015 *)
%o A253921 (PARI) Vec(-x*(x^4+50*x^3-262*x^2+50*x+1)/((x-1)*(x^2-22*x+1)*(x^2+22*x+1)) + O(x^100))
%o A253921 (Magma) I:=[1,51,271,24421,130461]; [n le 5 select I[n] else Self(n-1)+482*Self(n-2)-482*Self(n-3)-Self(n-4)+Self(n-5): n in [1..25]]; // _Vincenzo Librandi_, Jan 20 2015
%Y A253921 Cf. A000567, A005891, A253922, A253923.
%K A253921 nonn,easy
%O A253921 1,2
%A A253921 _Colin Barker_, Jan 19 2015