A052900 - OEIS

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

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OFFSET

0,4

LINKS

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 876

Index entries for linear recurrences with constant coefficients, signature (1,0,3).

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))

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 *)

CROSSREFS

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

Sequence in context: A225073 A152575 A170851 * A024947 A291407 A378153

Adjacent sequences: A052897 A052898 A052899 * A052901 A052902 A052903

KEYWORD

easy,nonn

AUTHOR

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

EXTENSIONS

More terms from James A. Sellers, Jun 06 2000

STATUS

approved