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

Author

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

Keywords

• easy
• nonn

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)

Programs

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 *)

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))

Extensions

More terms from James Sellers, Jun 05 2000