A008807 Expansion of (1+x^5)/((1-x^2)^2*(1-x^5)).

1, 0, 2, 0, 3, 2, 4, 4, 5, 6, 8, 8, 11, 10, 14, 14, 17, 18, 20, 22, 25, 26, 30, 30, 35, 36, 40, 42, 45, 48, 52, 54, 59, 60, 66, 68, 73, 76, 80, 84, 89, 92, 98, 100, 107, 110, 116, 120, 125, 130, 136, 140, 147, 150, 158, 162, 169, 174, 180, 186, 193, 198, 206

Offset

0,3

Links

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

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

Formula

G.f.: (1+x^5)/((1-x^2)^2*(1-x^5)). - G. C. Greubel, Sep 12 2019

Maple

seq(coeff(series((1+x^5)/((1-x^2)^2*(1-x^5)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 12 2019

Mathematica

CoefficientList[Series[(1+x^5)/((1-x^2)^2*(1-x^5)), {x, 0, 70}], x] (* or *) LinearRecurrence[{1, 1, -1, 0, 1, -1, -1, 1}, {1, 0, 2, 0, 3, 2, 4, 4}, 70] (* G. C. Greubel, Sep 12 2019 *)

Prog

(PARI) my(x='x+O('x^70)); Vec((1+x^5)/((1-x^2)^2*(1-x^5))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^5)/((1-x^2)^2*(1-x^5)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008807_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^5)/((1-x^2)^2*(1-x^5))).list()
A008807_list(70) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 0, 2, 0, 3, 2, 4, 4];; for n in [9..70] do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-5]-a[n-6]-a[n-7]+a[n-8]; od; a; # G. C. Greubel, Sep 12 2019

Crossrefs

Sequence in context: A289441 A291272 A291273 * A263149 A008819 A374018

Adjacent sequences: A008804 A008805 A008806 * A008808 A008809 A008810

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms added by G. C. Greubel, Sep 12 2019

Status

approved