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 A154997 #18 Dec 31 2023 11:36:08
%S A154997 1,1,11,96,906,8316,77076,711936,6583896,60861456,562685616,
%T A154997 5201957376,48092312736,444612597696,4110444968256,38001047740416,
%U A154997 351319635490176,3247949245153536,30027284535626496,277602184568365056
%N A154997 a(n) = 6*a(n-1) + 30*a(n-2), n>2; a(0)=1, a(1)=1, a(2)=11.
%C A154997 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 A154997 G. C. Greubel, <a href="/A154997/b154997.txt">Table of n, a(n) for n = 0..1000</a>
%H A154997 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,30).
%F A154997 G.f.: (1 -5*x -25*x^2)/(1 -6*x -30*x^2).
%F A154997 a(n+1) = Sum_{k=0..n} A154929(n,k)*5^(n-k).
%p A154997 m:=30; S:=series( (1-5*x-25*x^2)/(1-6*x-30*x^2), x, m+1):
%p A154997 seq(coeff(S, x, j), j=0..m); # _G. C. Greubel_, Apr 21 2021
%t A154997 Join[{1},LinearRecurrence[{6,30},{1,11},20]] (* _Harvey P. Dale_, Feb 07 2012 *)
%o A154997 (Magma) I:=[1,11]; [1] cat [n le 2 select I[n] else 6*(Self(n-1) +5*Self(n-2)): n in [1..30]]; // _G. C. Greubel_, Apr 21 2021
%o A154997 (Sage)
%o A154997 def A154996_list(prec):
%o A154997 P.<x> = PowerSeriesRing(ZZ, prec)
%o A154997 return P( (1-5*x-25*x^2)/(1-6*x-30*x^2) ).list()
%o A154997 A154996_list(30) # _G. C. Greubel_, Apr 21 2021
%Y A154997 Cf. A154996, A154999, A155000, A155001.
%K A154997 nonn
%O A154997 0,3
%A A154997 _Philippe Deléham_, Jan 18 2009