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 A253823 #8 Jan 22 2025 10:58:13
%S A253823 1,97921,1039585,130402572385,1384429704481,173658931280825761,
%T A253823 1843664419471976641,231264030011583194717761,
%U A253823 2455233718711319470593985,307977546462671843639087352385,3269669116478082433043125969441,410138010309759307549971991199125921
%N A253823 Octagonal numbers (A000567) which are also centered triangular numbers (A005448).
%H A253823 Colin Barker, <a href="/A253823/b253823.txt">Table of n, a(n) for n = 1..327</a>
%H A253823 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1331714,-1331714,-1,1).
%F A253823 a(n) = a(n-1)+1331714*a(n-2)-1331714*a(n-3)-a(n-4)+a(n-5).
%F A253823 G.f.: -x*(x^4+97920*x^3-390050*x^2+97920*x+1) / ((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)).
%e A253823 97921 is in the sequence because it is the 181st octagonal number and the 256th centered triangular number.
%t A253823 LinearRecurrence[{1,1331714,-1331714,-1,1},{1,97921,1039585,130402572385,1384429704481},20] (* _Harvey P. Dale_, Jan 22 2025 *)
%o A253823 (PARI) Vec(-x*(x^4+97920*x^3-390050*x^2+97920*x+1)/((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)) + O(x^100))
%Y A253823 Cf. A000567, A005448, A253821, A253822.
%K A253823 nonn,easy
%O A253823 1,2
%A A253823 _Colin Barker_, Jan 14 2015