A008801 Molien series for group [2,8]+ = 228.

1, 0, 2, 0, 3, 0, 4, 0, 6, 1, 8, 2, 10, 3, 12, 4, 15, 6, 18, 8, 21, 10, 24, 12, 28, 15, 32, 18, 36, 21, 40, 24, 45, 28, 50, 32, 55, 36, 60, 40, 66, 45, 72, 50, 78, 55, 84, 60, 91, 66, 98, 72, 105, 78, 112, 84, 120, 91, 128, 98, 136, 105, 144, 112, 153, 120, 162, 128, 171, 136, 180, 144, 190, 153

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

Formula

G.f.: (1+x^9)/((1-x^2)^2*(1-x^8)).

G.f.: (1-x+x^2)*(1-x^3+x^6)/( (1+x^2)*(1+x^4)*(1+x)^2*(1-x)^3 ). - R. J. Mathar, Dec 18 2014

Maple

seq(coeff(series((1+x^9)/((1-x^2)^2*(1-x^8)), x, n+1), x, n), n = 0..80);

Mathematica

CoefficientList[Series[(1+x^9)/((1-x^2)^2*(1-x^8)), {x, 0, 80}], x] (* G. C. Greubel, Sep 12 2019 *)

Prog

(PARI) my(x='x+O('x^80)); Vec((1+x^9)/((1-x^2)^2*(1-x^8))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^9)/((1-x^2)^2*(1-x^8)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008801_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^9)/((1-x^2)^2*(1-x^8))).list()
A008801_list(80) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 0, 6, 1, 8];; for n in [12..80] do a[n]:=a[n-1] +a[n-2]-a[n-3]+a[n-8]-a[n-9]-a[n-10]+a[n-11]; od; a; # G. C. Greubel, Sep 12 2019

Crossrefs

Sequence in context: A194749 A284969 A097852 * A073739 A223707 A046767

Adjacent sequences: A008798 A008799 A008800 * A008802 A008803 A008804

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved