A008720 Molien series for 3-dimensional group [2,5] = *225.

1, 0, 2, 0, 3, 1, 4, 2, 5, 3, 7, 4, 9, 5, 11, 7, 13, 9, 15, 11, 18, 13, 21, 15, 24, 18, 27, 21, 30, 24, 34, 27, 38, 30, 42, 34, 46, 38, 50, 42, 55, 46, 60, 50, 65, 55, 70, 60, 75, 65, 81, 70, 87, 75, 93, 81, 99, 87, 105, 93, 112, 99, 119, 105, 126, 112, 133, 119, 140, 126, 148, 133, 156

Offset

0,3

Links

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 223

Index entries for Molien series

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

Maple

1/((1-x^2)^2*(1-x^5)); 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, 1, 0, -2, 0, 1}, {1, 0, 2, 0, 3, 1, 4, 2, 5}, 80] (* Harvey P. Dale, Dec 10 2015 *)

Prog

(PARI) my(x='x+O('x^80)); Vec(1/((1-x^2)^2*(1-x^5))) \\ G. C. Greubel, Sep 09 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); Coefficients(R!( 1/((1-x^2)^2*(1-x^5)) )); // G. C. Greubel, Sep 09 2019
(Sage)
def A008720_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P(1/((1-x^2)^2*(1-x^5))).list()
A008720_list(80) # G. C. Greubel, Sep 09 2019
(GAP) a:=[1, 0, 2, 0, 3, 1, 4, 2, 5];; for n in [10..80] do a[n]:=2*a[n-2]-a[n-4] +a[n-5]-2*a[n-7]+a[n-9]; od; a; # G. C. Greubel, Sep 09 2019

Crossrefs

Sequence in context: A097065 A084964 A267182 * A340622 A263352 A008734

Adjacent sequences: A008717 A008718 A008719 * A008721 A008722 A008723

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms a(65) onward added by G. C. Greubel, Sep 09 2019

Status

approved