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 A090409 #18 Sep 06 2024 14:30:14
%S A090409 1,6,50,398,3186,25486,203890,1631118,13048946,104391566,835132530,
%T A090409 6681060238,53448481906,427587855246,3420702841970,27365622735758,
%U A090409 218924981886066,1751399855088526,14011198840708210,112089590725665678,896716725805325426,7173733806442603406
%N A090409 a(n) = (7*8^n + 2*(-1)^n)/9.
%H A090409 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,8).
%F A090409 a(n) = Sum_{j=0..2} Sum_{k=0..n} C(3*n+j, 3*k)/3.
%F A090409 a(n) = (A007613(n) + A082311(n) + A082365(n))/3.
%F A090409 G.f.: (-1+x)/((1+x)*(8*x-1)). - _R. J. Mathar_, Dec 10 2014
%F A090409 From _Elmo R. Oliveira_, Aug 18 2024: (Start)
%F A090409 E.g.f.: exp(-x)*(7*exp(9*x) + 2)/9.
%F A090409 a(n) = 7*a(n-1) + 8*a(n-2) for n > 1. (End)
%t A090409 LinearRecurrence[{7,8},{1,6},20] (* _Harvey P. Dale_, Aug 15 2016 *)
%Y A090409 First differences of A015565.
%Y A090409 Cf. A007613, A082311, A082365.
%K A090409 easy,nonn
%O A090409 0,2
%A A090409 _Paul Barry_, Nov 29 2003
%E A090409 a(20)-a(21) from _Elmo R. Oliveira_, Aug 18 2024