A008721 Molien series for 3-dimensional group [2,7] = *227.

1, 0, 2, 0, 3, 0, 4, 1, 5, 2, 6, 3, 7, 4, 9, 5, 11, 6, 13, 7, 15, 9, 17, 11, 19, 13, 21, 15, 24, 17, 27, 19, 30, 21, 33, 24, 36, 27, 39, 30, 42, 33, 46, 36, 50, 39, 54, 42, 58, 46, 62, 50, 66, 54, 70, 58, 75, 62, 80, 66, 85, 70, 90, 75, 95, 80, 100, 85, 105, 90, 111, 95, 117, 100, 123

Offset

0,3

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 224

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/((1-x^2)^2*(1-x^7)).

Maple

1/((1-x^2)^2*(1-x^7)); seq(coeff(series(%, x, n+1), x, n), n = 0..80); # modified by G. C. Greubel, Sep 09 2019

Mathematica

LinearRecurrence[{0, 2, 0, -1, 0, 0, 1, 0, -2, 0, 1}, {1, 0, 2, 0, 3, 0, 4, 1, 5, 2, 6}, 80] (* G. C. Greubel, Sep 09 2019 *)

Prog

(PARI) my(x='x+O('x^80)); Vec(1/((1-x^2)^2*(1-x^7))) \\ G. C. Greubel, Sep 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x^2)^2*(1-x^7)) )); // G. C. Greubel, Sep 09 2019
(Sage)
def A008721_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1-x^2)^2*(1-x^7)) ).list()
A008721_list(80) # G. C. Greubel, Sep 09 2019
(GAP) a:=[1, 0, 2, 0, 3, 0, 4, 1, 5, 2, 6];; 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 09 2019

Crossrefs

Sequence in context: A284976 A008743 A029179 * A008735 A239241 A263395

Adjacent sequences: A008718 A008719 A008720 * A008722 A008723 A008724

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms a(60) onward added by G. C. Greubel, Sep 09 2019

Status

approved