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 A253304 #9 Nov 05 2024 16:31:33
%S A253304 1,22,77,1376,4785,85302,296605,5287360,18384737,327731030,1139557101,
%T A253304 20314036512,70634155537,1259142532726,4378178086205,78046522992512,
%U A253304 271376407189185,4837625283003030,16820959067643277,299854721023195360,1042628085786694001
%N A253304 Numbers n such that the sum of the heptagonal numbers H(n) and H(n+1) is equal to the octagonal number O(m) for some m.
%C A253304 Also positive integers x in the solutions to 5*x^2-3*y^2+2*x+2*y+1 = 0, the corresponding values of y being A253305.
%H A253304 Colin Barker, <a href="/A253304/b253304.txt">Table of n, a(n) for n = 1..1000</a>
%H A253304 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,62,-62,-1,1).
%F A253304 a(n) = a(n-1)+62*a(n-2)-62*a(n-3)-a(n-4)+a(n-5).
%F A253304 G.f.: x*(3*x^3+7*x^2-21*x-1) / ((x-1)*(x^2-8*x+1)*(x^2+8*x+1)).
%e A253304 1 is in the sequence because H(1)+H(2) = 1+7 = 8 = O(2).
%t A253304 LinearRecurrence[{1,62,-62,-1,1},{1,22,77,1376,4785},30] (* _Harvey P. Dale_, Nov 05 2024 *)
%o A253304 (PARI) Vec(x*(3*x^3+7*x^2-21*x-1)/((x-1)*(x^2-8*x+1)*(x^2+8*x+1)) + O(x^100))
%Y A253304 Cf. A000566, A000567, A253305.
%K A253304 nonn,easy
%O A253304 1,2
%A A253304 _Colin Barker_, Dec 30 2014