A008798 Molien series for group [2,5]+ = 225.

1, 0, 2, 0, 3, 1, 5, 2, 7, 3, 10, 5, 13, 7, 16, 10, 20, 13, 24, 16, 29, 20, 34, 24, 39, 29, 45, 34, 51, 39, 58, 45, 65, 51, 72, 58, 80, 65, 88, 72, 97, 80, 106, 88, 115, 97, 125, 106, 135, 115, 146, 125, 157, 135, 168, 146, 180, 157, 192, 168, 205, 180, 218, 192, 231, 205, 245, 218, 259

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

Formula

G.f.: (1+x^6)/((1-x^2)^2*(1-x^5)).

a(n) = (17 + 6*n + 2*n^2 + 5*(-1)^n*(3 + 2*n) + 8*A080891(n+4))/40.

Maple

A080891 := proc(n) op((n mod 5)+1, [0, 1, -1, -1, 1]) ; end proc:
A008798 := proc(n) 17/40+3*n/20+n^2/20+(-1)^n*(3/8+n/4) +A080891(n+4)/5; end proc:

Mathematica

CoefficientList[Series[(1+x^6)/((1-x^2)^2*(1-x^5)), {x, 0, 70}], x] (* G. C. Greubel, Sep 12 2019 *)

Prog

(PARI) my(x='x+O('x^70)); Vec((1+x^6)/((1-x^2)^2*(1-x^5))) \\ G. C. Greubel, Sep 12 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^6)/((1-x^2)^2*(1-x^5)) )); // G. C. Greubel, Sep 12 2019
(SageMath)
def A008798_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^6)/((1-x^2)^2*(1-x^5))).list()
A008798_list(70) # G. C. Greubel, Sep 12 2019
(GAP) a:=[1, 0, 2, 0, 3, 1, 5, 2, 7];; for n in [10..70] 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 12 2019

Crossrefs

Sequence in context: A162170 A266770 A282892 * A005290 A326440 A166117

Adjacent sequences: A008795 A008796 A008797 * A008799 A008800 A008801

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