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 A322707 #28 Mar 16 2023 08:17:10 %S A322707 0,5,120,2645,58080,1275125,27994680,614607845,13493377920, %T A322707 296239706405,6503780163000,142786923879605,3134808545188320, %U A322707 68823001070263445,1510971215000607480,33172543728943101125,728284990821747617280,15989097254349504479045 %N A322707 a(0)=0, a(1)=5 and a(n) = 22*a(n-1) - a(n-2) + 10 for n > 1. %C A322707 Solutions to X*(X+1)=30*Y^2 with Y=A077421. - _R. J. Mathar_, Mar 14 2023 %H A322707 Colin Barker, <a href="/A322707/b322707.txt">Table of n, a(n) for n = 0..700</a> %H A322707 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (23,-23,1). %F A322707 sqrt(a(n)+1) + sqrt(a(n)) = (sqrt(6) + sqrt(5))^n. %F A322707 sqrt(a(n)+1) - sqrt(a(n)) = (sqrt(6) - sqrt(5))^n. %F A322707 a(n) = 23*a(n-1) - 23*a(n-2) + a(n-3) for n > 2. %F A322707 From _Colin Barker_, Dec 24 2018: (Start) %F A322707 G.f.: 5*x*(1 + x) / ((1 - x)*(1 - 22*x + x^2)). %F A322707 a(n) = ((11+2*sqrt(30))^(-n) * (-1+(11+2*sqrt(30))^n)^2) / 4. %F A322707 (End) %F A322707 2*a(n) = A077422(n)-1. - _R. J. Mathar_, Mar 16 2023 %e A322707 (sqrt(6) + sqrt(5))^2 = 11 + 2*sqrt(30) = sqrt(121) + sqrt(120). So a(2) = 120. %o A322707 (PARI) concat(0, Vec(5*x*(1 + x) / ((1 - x)*(1 - 22*x + x^2)) + O(x^20))) \\ _Colin Barker_, Dec 24 2018 %Y A322707 Row 5 of A322699. %Y A322707 Cf. A188930 (sqrt(5)+sqrt(6)). %K A322707 nonn,easy %O A322707 0,2 %A A322707 _Seiichi Manyama_, Dec 24 2018