A008797 Molien series for group [2,4]+ = 224.

1, 0, 2, 0, 4, 1, 6, 2, 9, 4, 12, 6, 16, 9, 20, 12, 25, 16, 30, 20, 36, 25, 42, 30, 49, 36, 56, 42, 64, 49, 72, 56, 81, 64, 90, 72, 100, 81, 110, 90, 121, 100, 132, 110, 144, 121, 156, 132, 169, 144, 182, 156, 196, 169, 210, 182, 225, 196, 240, 210, 256, 225, 272, 240, 289, 256, 306, 272

Offset

0,3

Links

Vincenzo Librandi, 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,-1,1,-1,-1,1).

Formula

G.f.: (1+x^5)/((1-x^2)^2*(1-x^4)).

a(n) = floor((n^2 + 3*n + 11 + 5*(n+1)*(-1)^n)/16). - Tani Akinari, Jul 07 2014

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

Maple

seq(coeff(series((1+x^5)/((1-x^2)^2*(1-x^4)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 11 2019

Mathematica

CoefficientList[Series[(1+x^5)/((1-x^2)^2(1-x^4)), {x, 0, 70}], x] (* Vincenzo Librandi, Jul 08 2014 *)
LinearRecurrence[{1, 1, -1, 1, -1, -1, 1}, {1, 0, 2, 0, 4, 1, 6}, 70] (* Harvey P. Dale, May 15 2017 *)

Prog

(PARI) Vec((1+x^5)/(1-x^2)^2/(1-x^4)+ O(x^70)) \\ Michel Marcus, Jul 07 2014
(Magma) [Floor((n^2+3*n+11+5*(n+1)*(-1)^n)/16): n in [0..70]]; // Vincenzo Librandi, Jul 08 2014
(Sage)
def A008797_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^5)/((1-x^2)^2*(1-x^4))).list()
A008797_list(70) # G. C. Greubel, Sep 11 2019
(GAP) a:=[1, 0, 2, 0, 4, 1, 6];; for n in [8..70] do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-4]-a[n-5]-a[n-6]+a[n-7]; od; a; # G. C. Greubel, Sep 11 2019

Crossrefs

Sequence in context: A056737 A289144 A350576 * A239004 A168036 A371499

Adjacent sequences: A008794 A008795 A008796 * A008798 A008799 A008800

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 11 2019

Status

approved