A052900 Expansion of (1-x)/(1-x-3x^3).

1, 0, 0, 3, 3, 3, 12, 21, 30, 66, 129, 219, 417, 804, 1461, 2712, 5124, 9507, 17643, 33015, 61536, 114465, 213510, 398118, 741513, 1382043, 2576397, 4800936, 8947065, 16676256, 31079064, 57920259, 107949027, 201186219, 374946996

Offset: 0

Author

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

Keywords

• easy
• nonn

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 876
• Index entries for linear recurrences with constant coefficients, signature (1,0,3).

Crossrefs

a(n) = 3*A084386(n-3), also first differences of A084386.

Programs

Maple

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

Mathematica

CoefficientList[Series[(1-x)/(1-x-3x^3),{x,0,40}],x] (* or *) LinearRecurrence[{1,0,3},{1,0,0},40] (* Harvey P. Dale, Aug 05 2021 *)

Formula

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

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

Sum(-1/85*(2+9*_alpha^2-29*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z+3*_Z^3))

Extensions

More terms from James Sellers, Jun 06 2000