A008800 Molien series for group [2,7]+ = 227.

1, 0, 2, 0, 3, 0, 4, 1, 6, 2, 8, 3, 10, 4, 13, 6, 16, 8, 19, 10, 22, 13, 26, 16, 30, 19, 34, 22, 39, 26, 44, 30, 49, 34, 54, 39, 60, 44, 66, 49, 72, 54, 79, 60, 86, 66, 93, 72, 100, 79, 108, 86, 116, 93, 124, 100, 133, 108, 142, 116, 151, 124, 160, 133, 170, 142, 180, 151, 190, 160, 201, 170

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,-1,0,0,1,0,-2,0,1).

Formula

G.f.: (1+x^8)/((1-x^2)^2 * (1-x^7)).

Maple

seq(coeff(series((1+x^8)/((1-x^2)^2*(1-x^7)), x, n+1), x, n), n = 0..80);

Mathematica

CoefficientList[Series[(1+x^8)/((1-x^2)^2*(1-x^7)), {x, 0, 80}], x] (* G. C. Greubel, Sep 12 2019 *)
LinearRecurrence[{0, 2, 0, -1, 0, 0, 1, 0, -2, 0, 1}, {1, 0, 2, 0, 3, 0, 4, 1, 6, 2, 8}, 80] (* Harvey P. Dale, Jul 07 2021 *)

Prog

(PARI) my(x='x+O('x^80)); Vec((1+x^8)/((1-x^2)^2*(1-x^7))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( (1+x^8)/((1-x^2)^2*(1-x^7)) )); // G. C. Greubel, Sep 12 2019
(Sage)
def A008800_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^8)/((1-x^2)^2*(1-x^7))).list()
A008800_list(80) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 1, 6, 2, 8];; for n in [12..80] do a[n]:=2*a[n-2] -a[n-4]+a[n-7]-2*a[n-9]+a[n-11]; od; a; # G. C. Greubel, Sep 12 2019

Crossrefs

Sequence in context: A263395 A240139 A360952 * A274096 A318518 A008808

Adjacent sequences: A008797 A008798 A008799 * A008801 A008802 A008803

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Definition clarified by N. J. A. Sloane, Feb 02 2018

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

Status

approved