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 A322708 #23 Mar 14 2023 12:57:32
%S A322708 0,6,168,4374,113568,2948406,76545000,1987221606,51591216768,
%T A322708 1339384414374,34772403556968,902743108066806,23436548406180000,
%U A322708 608447515452613206,15796198853361763368,410092722671953234374,10646614590617422330368,276401886633381027355206
%N A322708 a(0)=0, a(1)=6 and a(n) = 26*a(n-1) - a(n-2) + 12 for n > 1.
%C A322708 Solutions to X*(X+1)=42*Y^2 with Y=A097309. - _R. J. Mathar_, Mar 14 2023
%H A322708 Seiichi Manyama, <a href="/A322708/b322708.txt">Table of n, a(n) for n = 0..500</a>
%H A322708 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (27,-27,1).
%F A322708 sqrt(a(n)+1) + sqrt(a(n)) = (sqrt(7) + sqrt(6))^n.
%F A322708 sqrt(a(n)+1) - sqrt(a(n)) = (sqrt(7) - sqrt(6))^n.
%F A322708 a(n) = 27*a(n-1) - 27*a(n-2) + a(n-3) for n > 2.
%F A322708 From _Colin Barker_, Dec 24 2018: (Start)
%F A322708 G.f.: 6*x*(1 + x) / ((1 - x)*(1 - 26*x + x^2)).
%F A322708 a(n) = ((13+2*sqrt(42))^(-n) * (-1+(13+2*sqrt(42))^n)^2) / 4.
%F A322708 (End)
%F A322708 2*a(n) = A097308(n)-1. - _R. J. Mathar_, Mar 14 2023
%e A322708 (sqrt(7) + sqrt(6))^2 = 13 + 2*sqrt(42) = sqrt(169) + sqrt(168). So a(2) = 168.
%t A322708 LinearRecurrence[{27,-27,1},{0,6,168},20] (* _Harvey P. Dale_, Apr 30 2022 *)
%o A322708 (PARI) concat(0, Vec(6*x*(1 + x) / ((1 - x)*(1 - 26*x + x^2)) + O(x^20))) \\ _Colin Barker_, Dec 24 2018
%Y A322708 Row 6 of A322699.
%K A322708 nonn,easy
%O A322708 0,2
%A A322708 _Seiichi Manyama_, Dec 24 2018