A144701 Hankel transform of expansion of 1/c(x)^3, c(x) the g.f. of A000108.

1, -9, 26, -25, -36, 133, -132, -81, 375, -374, -144, 806, -805, -225, 1480, -1479, -324, 2451, -2450, -441, 3773, -3772, -576, 5500, -5499, -729, 7686, -7685, -900, 10385, -10384, -1089, 13651, -13650, -1296, 17538, -17537

Offset

0,2

Comments

Hankel transform of A115142.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-4,-10,-16,-19,-16,-10,-4,-1).

Formula

G.f.: (1+x)*(1-x)*(1-5*x+x^2)/(1+x+x^2)^4.

a(n) = (6 - 7*n - 9*n^2 - 2*n^3)*cos(2*Pi*n/3)/6 - sqrt(3)*(42 + 55*n + 21*n^2 + 2*n^3)*sin(2*Pi*n/3)/18.

Mathematica

LinearRecurrence[{-4, -10, -16, -19, -16, -10, -4, -1}, {1, -9, 26, -25, -36, 133, -132, -81}, 40] (* G. C. Greubel, Jun 16 2022 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x^2)*(1-5*x+x^2)/(1+x+x^2)^4 )); // G. C. Greubel, Jun 16 2022
(SageMath)
def A144701_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1-x^2)*(1-5*x+x^2)/(1+x+x^2)^4 ).list()
A144701_list(40) # G. C. Greubel, Jun 16 2022

Crossrefs

Cf. A000108, A099504, A115142, A128504.

Sequence in context: A352788 A144114 A209969 * A255107 A022421 A075395

Adjacent sequences: A144698 A144699 A144700 * A144702 A144703 A144704

Keyword

easy,sign

Author

Paul Barry, Sep 19 2008

Status

approved