A008808 Expansion of (1+x^7)/((1-x^2)^2*(1-x^7)).

1, 0, 2, 0, 3, 0, 4, 2, 5, 4, 6, 6, 7, 8, 10, 10, 13, 12, 16, 14, 19, 18, 22, 22, 25, 26, 28, 30, 33, 34, 38, 38, 43, 42, 48, 48, 53, 54, 58, 60, 63, 66, 70, 72, 77, 78, 84, 84, 91, 92, 98, 100, 105, 108, 112, 116, 121, 124, 130, 132, 139, 140, 148, 150, 157

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,-1,0,0,0,1,-1,-1,1).

Formula

G.f.: (1 -x +x^2 -x^3 -x^4 +x^5 -x^6)/( (1+x)*(1+x+x^2+x^3+x^4+x^5+x^6)*(1-x)^3 ). - R. J. Mathar, Feb 06 2015

Maple

seq(coeff(series((1+x^7)/((1-x^2)^2*(1-x^7)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 12 2019

Mathematica

LinearRecurrence[{1, 1, -1, 0, 0, 0, 1, -1, -1, 1}, {1, 0, 2, 0, 3, 0, 4, 2, 5, 4}, 70] (* G. C. Greubel, Sep 12 2019 *)

Prog

(PARI) a(n)=(4*((-1)^(n%7)-1)*(n%7+1)+2*n^2+8*n+55+49*(-1)^n)\56  \\ Tani Akinari, Jul 24 2013
(PARI) Vec((1+x^7)/(1-x^2)^2/(1-x^7) + O(x^70)) \\ Michel Marcus, Feb 06 2015
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^7)/((1-x^2)^2*(1-x^7)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008808_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^7)/((1-x^2)^2*(1-x^7))).list()
A008808_list(70) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 2, 5, 4];; for n in [11..70] do a[n]:=a[n-1]+a[n-2] -a[n-3]+a[n-7]-a[n-8]-a[n-9]+a[n-10]; od; a; # G. C. Greubel, Sep 12 2019

Crossrefs

Sequence in context: A008800 A274096 A318518 * A008820 A357475 A066682

Adjacent sequences: A008805 A008806 A008807 * A008809 A008810 A008811

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved