A052972 Expansion of (1-x^3)/(1-x-x^2-x^3+x^5).

1, 1, 2, 3, 6, 10, 18, 32, 57, 101, 180, 320, 569, 1012, 1800, 3201, 5693, 10125, 18007, 32025, 56956, 101295, 180151, 320395, 569816, 1013406, 1802322, 3205393, 5700726, 10138625, 18031338, 32068367, 57032937, 101431916, 180394595

Offset

0,3

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1044

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

Formula

G.f.: -(-1+x^3)/(1-x^3-x-x^2+x^5)

Recurrence: {a(1)=1, a(0)=1, a(3)=3, a(2)=2, a(4)=6, a(n)-a(n+2)-a(n+3)-a(n+4)+a(n+5)=0}

Sum(-1/7031*(-1007-901*_alpha^2-1879*_alpha+1187*_alpha^4-95*_alpha^3)*_alpha^(-1-n), _alpha=RootOf(1-_Z^3-_Z-_Z^2+_Z^5))

Maple

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

Mathematica

CoefficientList[Series[(1-x^3)/(1-x-x^2-x^3+x^5), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, 1, 1, 0, -1}, {1, 1, 2, 3, 6}, 50] (* Harvey P. Dale, Sep 18 2016 *)

Crossrefs

Sequence in context: A357451 A224342 A181649 * A018166 A144026 A054152

Adjacent sequences: A052969 A052970 A052971 * A052973 A052974 A052975

Keyword

easy,nonn

Author

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

Extensions

More terms from James A. Sellers, Jun 05 2000

Status

approved