A008802 Molien series for group [2,9]+ = 229.

1, 0, 2, 0, 3, 0, 4, 0, 5, 1, 7, 2, 9, 3, 11, 4, 13, 5, 16, 7, 19, 9, 22, 11, 25, 13, 28, 16, 32, 19, 36, 22, 40, 25, 44, 28, 49, 32, 54, 36, 59, 40, 64, 44, 69, 49, 75, 54, 81, 59, 87, 64, 93, 69, 100, 75, 107, 81, 114, 87, 121, 93, 128, 100, 136, 107, 144, 114

Offset

0,3

Links

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

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1,0,0,0,0,1,0,-2,0,1).

Formula

G.f.: (1+x^10)/((1-x^2)^2*(1-x^9)).

Maple

seq(coeff(series((1+x^10)/((1-x^2)^2*(1-x^9)), x, n+1), x, n), n = 0..80);

Mathematica

CoefficientList[Series[(1+x^10)/(1-x^2)^2/(1-x^9), {x, 0, 80}], x] (* Harvey P. Dale, Nov 28 2012 *)
LinearRecurrence[{0, 2, 0, -1, 0, 0, 0, 0, 1, 0, -2, 0, 1}, {1, 0, 2, 0, 3, 0, 4, 0, 5, 1, 7, 2}, 80] (* G. C. Greubel, Sep 12 2019 *)

Prog

(PARI) my(x='x+O('x^80)); Vec((1+x^10)/((1-x^2)^2*(1-x^9))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^10)/((1-x^2)^2*(1-x^9)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008802_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^10)/((1-x^2)^2*(1-x^9))).list()
A008802_list(80) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 0, 5, 1, 7, 2];; for n in [13..80] do a[n]:=2*a[n-2] -a[n-4]+a[n-9]-2*a[n-10]+a[n-12]; od; a; # G. C. Greubel, Sep 12 2019

Crossrefs

Sequence in context: A008736 A263396 A029180 * A008809 A008821 A194749

Adjacent sequences: A008799 A008800 A008801 * A008803 A008804 A008805

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved