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 A133409 #11 Mar 10 2023 13:31:39
%S A133409 0,0,0,0,1,4,13,39,117,351,1054,3163,9490,28470,85410,256230,768691,
%T A133409 2306074,6918223,20754669,62264007,186792021,560376064,1681128193,
%U A133409 5043384580,15130153740,45390461220,136171383660
%N A133409 Zero followed by partial sums of A133405.
%H A133409 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-1,4,-3).
%F A133409 a(n+1)-3*a(n) = A088911(n+3).
%F A133409 a(n) = 4*a(n-1)-3*a(n-2)-a(n-3)+4*a(n-4)-3*a(n-5).
%F A133409 O.g.f.: x^4/((3*x-1)*(1+x)*(x^2-x+1)*(x-1)). - _R. J. Mathar_, Jul 16 2008
%t A133409 Join[{0},Accumulate[LinearRecurrence[{3,0,-1,3},{0,0,0,1},40]]] (* or *) LinearRecurrence[{4,-3,-1,4,-3},{0,0,0,0,1},40] (* _Harvey P. Dale_, Dec 24 2013 *)
%Y A133409 Cf. A088911, A133405.
%K A133409 nonn
%O A133409 0,6
%A A133409 _Paul Curtz_, Nov 25 2007
%E A133409 Edited and extended by _R. J. Mathar_, Jul 16 2008