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 A052971 #28 Jul 02 2025 16:01:58
%S A052971 1,1,2,6,12,26,60,132,292,652,1448,3216,7152,15896,35328,78528,174544,
%T A052971 387952,862304,1916640,4260096,9468896,21046464,46779840,103977280,
%U A052971 231109696,513686144,1141767168,2537799168,5640751232,12537664512,27867393024,61940690176
%N A052971 Expansion of (1-x)/(1-2*x-2*x^3+2*x^4).
%C A052971 a(n) is the number of compositions of n using three colors of 3. Compare to A077998 which gives the number of compositions of n using two colors of 2. - _Greg Dresden_ and Yushu Fan, Aug 15 2023
%H A052971 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1043">Encyclopedia of Combinatorial Structures 1043</a>
%H A052971 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,2,-2).
%F A052971 G.f.: -(-1+x)/(1-2*x-2*x^3+2*x^4).
%F A052971 Recurrence: {a(1)=1, a(0)=1, a(3)=6, a(2)=2, 2*a(n)-2*a(n+1)-2*a(n+3)+a(n+4)=0}.
%F A052971 Sum(-1/227*(-29-50*_alpha+45*_alpha^3-14*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-2*_Z^3+2*_Z^4)).
%p A052971 spec := [S,{S=Sequence(Prod(Union(Prod(Union(Z,Z),Z),Sequence(Z)),Z))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
%t A052971 CoefficientList[Series[(1-x)/(1-2x-2x^3+2x^4),{x,0,30}],x] (* or *) LinearRecurrence[{2,0,2,-2},{1,1,2,6},32] (* _Harvey P. Dale_, Jul 23 2012 *)
%Y A052971 Cf. A077998.
%K A052971 easy,nonn
%O A052971 0,3
%A A052971 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052971 More terms from _James Sellers_, Jun 06 2000