A052969 Expansion of (1-x)/(1-x-2x^2+x^4).

1, 0, 2, 2, 5, 9, 17, 33, 62, 119, 226, 431, 821, 1564, 2980, 5677, 10816, 20606, 39258, 74793, 142493, 271473, 517201, 985354, 1877263, 3576498, 6813823, 12981465, 24731848, 47118280, 89768153, 171023248, 325827706, 620755922, 1182643181

Offset

0,3

Links

Table of n, a(n) for n=0..34.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1041

Index entries for linear recurrences with constant coefficients, signature (1,2,0,-1).

Formula

G.f.: -(-1+x)/(1-2*x^2+x^4-x).

Recurrence: {a(0)=1, a(1)=0, a(2)=2, a(3)=2, a(n)-2*a(n+2)-a(n+3)+a(n+4)=0}.

Sum_(1/283*(29*_alpha+28*_alpha^3-76*_alpha^2+55)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z^2+_Z^4-_Z)).

a(n)+a(n-1) = A052535(n). - R. J. Mathar, Nov 28 2011

Maple

spec := [S, {S=Sequence(Prod(Union(Prod(Union(Sequence(Z), Z), Z), Z), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);

Mathematica

CoefficientList[Series[(1-x)/(1-x-2x^2+x^4), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 2, 0, -1}, {1, 0, 2, 2}, 40] (* Harvey P. Dale, Oct 20 2017 *)

Crossrefs

Cf. A052535.

Sequence in context: A212812 A214727 A302483 * A002990 A060405 A326493

Adjacent sequences: A052966 A052967 A052968 * A052970 A052971 A052972

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

More terms from James A. Sellers, Jun 05 2000

Status

approved