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 A052900 #17 Jul 02 2025 16:01:58
%S A052900 1,0,0,3,3,3,12,21,30,66,129,219,417,804,1461,2712,5124,9507,17643,
%T A052900 33015,61536,114465,213510,398118,741513,1382043,2576397,4800936,
%U A052900 8947065,16676256,31079064,57920259,107949027,201186219,374946996
%N A052900 Expansion of (1-x)/(1-x-3x^3).
%H A052900 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=876">Encyclopedia of Combinatorial Structures 876</a>
%H A052900 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,3).
%F A052900 G.f.: (-1+x)/(-1+x+3*x^3)
%F A052900 Recurrence: {a(1)=0, a(0)=1, a(2)=0, 3*a(n)+a(n+2)-a(n+3)=0}
%F A052900 Sum(-1/85*(2+9*_alpha^2-29*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+3*_Z^3))
%p A052900 spec := [S,{S=Sequence(Prod(Union(Z,Z,Z),Sequence(Z),Z,Z))},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t A052900 CoefficientList[Series[(1-x)/(1-x-3x^3),{x,0,40}],x] (* or *) LinearRecurrence[{1,0,3},{1,0,0},40] (* _Harvey P. Dale_, Aug 05 2021 *)
%Y A052900 a(n) = 3*A084386(n-3), also first differences of A084386.
%K A052900 easy,nonn
%O A052900 0,4
%A A052900 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052900 More terms from _James Sellers_, Jun 06 2000