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
KEYWORD
easy,sign
AUTHOR
Paul Barry, Sep 19 2008
STATUS
approved