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 A052994 #22 Jul 02 2025 16:01:58
%S A052994 0,2,2,6,12,28,62,140,314,706,1586,3564,8008,17994,40432,90850,204138,
%T A052994 458694,1030676,2315908,5203798,11692828,26273546,59036122,132652962,
%U A052994 298068500,669753840,1504923218,3381531776,7598232930,17073074418
%N A052994 Expansion of 2x(1-x)/(1-2x-x^2+x^3).
%H A052994 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1071">Encyclopedia of Combinatorial Structures 1071</a>
%H A052994 Sergey Kitaev, Jeffrey Remmel, <a href="http://arxiv.org/abs/1304.4286">(a,b)-rectangle patterns in permutations and words</a>, arXiv:1304.4286 [math.CO], 2013.
%H A052994 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-1).
%F A052994 G.f.: -2*x*(-1+x)/(x^3-x^2-2*x+1)
%F A052994 Recurrence: {a(0)=0, a(1)=2, a(2)=2, a(n)-a(n+1)-2*a(n+2)+a(n+3)=0}
%F A052994 Sum(2/7*(-_alpha+_alpha^2+1)*_alpha^(-1-n), _alpha=RootOf(_Z^3-_Z^2-2*_Z+1))
%p A052994 spec := [S,{S=Prod(Sequence(Prod(Union(Sequence(Z),Z),Z)),Union(Z,Z))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
%o A052994 (PARI) concat(0, Vec(-2*x*(-1+x)/(x^3-x^2-2*x+1) + O(x^40))) \\ _Michel Marcus_, Mar 19 2015
%Y A052994 Equals 2 * A006356(n-2), n>1.
%K A052994 easy,nonn
%O A052994 0,2
%A A052994 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052994 More terms from _James Sellers_, Jun 05 2000