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 A154996 #16 Dec 31 2023 11:36:04
%S A154996 1,1,9,65,505,3825,29225,222625,1697625,12940625,98655625,752090625,
%T A154996 5733565625,43709640625,333219515625,2540290390625,19365842265625,
%U A154996 147635019140625,1125491941015625,8580160087890625,65410639259765625
%N A154996 a(n) = 5*a(n-1) + 20*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=9.
%C A154996 The sequences A155001, A155000, A154999, A154997 and A154996 have a common form: a(0)=a(1)=1, a(2)= 2*b+1, a(n) = (b+1)*(a(n-1) + b*a(n-2)), with b some constant. The generating function of these is (1 - b*x - b^2*x^2)/(1 - (b+1)*x - b*(1+b)*x^2). - _R. J. Mathar_, Jan 20 2009
%H A154996 G. C. Greubel, <a href="/A154996/b154996.txt">Table of n, a(n) for n = 0..1000</a>
%H A154996 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,20).
%F A154996 G.f.: (1 -4*x -16*x^2)/(1 -5*x -20*x^2).
%F A154996 a(n+1) = Sum_{k=0..n} A154929(n,k)*4^(n-k).
%p A154996 m:=30; S:=series( (1-4*x-16*x^2)/(1-5*x-20*x^2), x, m+1):
%p A154996 seq(coeff(S, x, j), j=0..m); # _G. C. Greubel_, Apr 21 2021
%t A154996 Join[{1},LinearRecurrence[{5,20},{1,9},20]] (* _Harvey P. Dale_, Jan 19 2012 *)
%o A154996 (Magma) I:=[1,9]; [1] cat [n le 2 select I[n] else 5*(Self(n-1) +4*Self(n-2)): n in [1..30]]; // _G. C. Greubel_, Apr 21 2021
%o A154996 (Sage)
%o A154996 def A154996_list(prec):
%o A154996 P.<x> = PowerSeriesRing(ZZ, prec)
%o A154996 return P( (1-4*x-16*x^2)/(1-5*x-20*x^2) ).list()
%o A154996 A154996_list(30) # _G. C. Greubel_, Apr 21 2021
%Y A154996 Cf. A154997, A154999, A155000, A155001.
%K A154996 nonn
%O A154996 0,3
%A A154996 _Philippe Deléham_, Jan 18 2009