A052988 Expansion of (1-x^2)/(1-2x-2x^2+x^3+x^4).

1, 2, 5, 13, 33, 85, 218, 560, 1438, 3693, 9484, 24356, 62549, 160633, 412524, 1059409, 2720684, 6987029, 17943493, 46080951, 118341175, 303913730, 780485366, 2004376066, 5147467959, 13219288954, 33948652394, 87184038671

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1062

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

Formula

G.f.: -(-1+x^2)/(1-2*x-2*x^2+x^3+x^4)

Recurrence: {a(0)=1, a(1)=2, a(2)=5, a(3)=13, a(n)+a(n+1)-2*a(n+2)-2*a(n+3)+a(n+4)}

Sum(-1/331*(-49-147*_alpha+25*_alpha^2+76*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-2*_Z-2*_Z^2+_Z^3+_Z^4))

Maple

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

Mathematica

CoefficientList[Series[(1-x^2)/(1-2x-2x^2+x^3+x^4), {x, 0, 30}], x] (* or *) LinearRecurrence[{2, 2, -1, -1}, {1, 2, 5, 13}, 30] (* Harvey P. Dale, Sep 21 2016 *)

Crossrefs

Sequence in context: A077986 A007020 A080888 * A001429 A148288 A320813

Adjacent sequences: A052985 A052986 A052987 * A052989 A052990 A052991

Keyword

easy,nonn

Author

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

Extensions

More terms from James A. Sellers, Jun 05 2000

Status

approved