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 A253673 #12 Aug 07 2023 10:17:10
%S A253673 1,16,65,1520,6321,148896,619345,14590240,60689441,1429694576,
%T A253673 5946945825,140095478160,582740001361,13727927165056,57102573187505,
%U A253673 1345196766697280,5595469432374081,131815555209168336,548298901799472385,12916579213731799600
%N A253673 Indices of centered triangular numbers (A005448) that are also centered octagonal numbers (A016754).
%C A253673 Also positive integers x in the solutions to 3*x^2 - 8*y^2 - 3*x + 8*y = 0, the corresponding values of y being A253674.
%C A253673 Also indices of centered square numbers (A001844) that are also octagonal numbers (A000567). - _Colin Barker_, Feb 10 2015
%H A253673 Colin Barker, <a href="/A253673/b253673.txt">Table of n, a(n) for n = 1..1000</a>
%H A253673 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,98,-98,-1,1).
%F A253673 a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5).
%F A253673 G.f.: x*(3*x-1)*(5*x^2+18*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).
%e A253673 16 is in the sequence because the 16th centered triangular number is 361, which is also the 10th centered octagonal number.
%t A253673 LinearRecurrence[{1,98,-98,-1,1},{1,16,65,1520,6321},20] (* _Harvey P. Dale_, Aug 07 2023 *)
%o A253673 (PARI) Vec(x*(3*x-1)*(5*x^2+18*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))
%Y A253673 Cf. A005448, A016754, A253674, A253675.
%Y A253673 Cf. A000567, A001844, A254895, A254896.
%K A253673 nonn,easy
%O A253673 1,2
%A A253673 _Colin Barker_, Jan 08 2015