A108629 Expansion of g.f.: (1+x - sqrt(1-2*x-3*x^2-4*x^3))/(2+2*x+2*x^2).

1, 0, 1, 2, 4, 11, 28, 75, 207, 579, 1647, 4744, 13807, 40550, 120016, 357613, 1071916, 3229870, 9777767, 29724593, 90705886, 277744244, 853123473, 2627968236, 8116487286, 25128482223, 77971354506, 242439732171

Offset

1,4

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

Conjecture D-finite with recurrence: n*a(n) = (n-3)*a(n-1) +4*(n-3)*a(n-2) +3*(3*n-10)*a(n-3) +(7*n-27)*a(n-4) +2*(2*n-9)*a(n-5). - R. J. Mathar, Jan 24 2020

Mathematica

Rest@CoefficientList[Series[(1+x -Sqrt[1-2*x-3*x^2-4*x^3])/(2+2*x +2*x^2), {x, 0, 40}], x] (* G. C. Greubel, Oct 06 2023 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!( (1+x-Sqrt(1-2*x-3*x^2-4*x^3))/(2+2*x+2*x^2) )); // G. C. Greubel, Oct 06 2023
(SageMath)
def A108629_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x-sqrt(1-2*x-3*x^2-4*x^3))/(2+2*x+2*x^2) ).list()
a=A108629_list(41); a[1:] # G. C. Greubel, Oct 06 2023

Crossrefs

Cf. A039983.

Sequence in context: A122423 A099016 A026122 * A007048 A148132 A032101

Adjacent sequences: A108626 A108627 A108628 * A108630 A108631 A108632

Keyword

nonn

Author

Christian G. Bower, Jun 12 2005

Status

approved