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 A253689 #11 Sep 08 2022 08:46:10
%S A253689 1,316,7246,3818431,87657571,46195373386,1060481282176,
%T A253689 558871623400861,12829702464103141,6761228853708238456,
%U A253689 155213739350238513106,81797346113290645435291,1877775805829483067448711,989584286517361374767907526,22717331543711346799755988036
%N A253689 Centered triangular numbers (A005448) which are also centered heptagonal numbers (A069099).
%H A253689 Colin Barker, <a href="/A253689/b253689.txt">Table of n, a(n) for n = 1..490</a>
%H A253689 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,12098,-12098,-1,1).
%F A253689 a(n) = a(n-1)+12098*a(n-2)-12098*a(n-3)-a(n-4)+a(n-5).
%F A253689 G.f.: -x*(x^4+315*x^3-5168*x^2+315*x+1) / ((x-1)*(x^2-110*x+1)*(x^2+110*x+1)).
%e A253689 316 is in the sequence because it is the 15th centered triangular number and the 10th centered heptagonal number.
%t A253689 LinearRecurrence[{1, 12098, -12098, -1, 1}, {1, 316, 7246, 3818431, 87657571}, 20] (* or *) CoefficientList[Series[(x^4 + 315 x^3 - 5168 x^2 + 315 x + 1) / ((1 - x) (x^2 - 110 x + 1)(x^2 + 110 x + 1)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jan 10 2015 *)
%o A253689 (PARI) Vec(-x*(x^4+315*x^3-5168*x^2+315*x+1)/((x-1)*(x^2-110*x+1)*(x^2+110*x+1)) + O(x^100))
%o A253689 (Magma) I:=[1,316,7246,3818431,87657571]; [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 10 2015
%Y A253689 Cf. A005448, A069099, A253476, A253477.
%K A253689 nonn,easy
%O A253689 1,2
%A A253689 _Colin Barker_, Jan 09 2015