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

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1041
• Index entries for linear recurrences with constant coefficients, signature (1,2,0,-1).

Crossrefs

Cf. A052535.

Programs

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 *)

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

Extensions

More terms from James Sellers, Jun 05 2000