A005868 Molien series for 3-dimensional representation of Z2 X (double cover of A6), u.g.g.r. # 27 of Shephard and Todd.

1, 0, 1, 0, 2, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 1, 7, 1, 8, 2, 10, 2, 11, 3, 13, 4, 14, 5, 16, 6, 18, 7, 20, 8, 22, 10, 24, 11, 26, 13, 29, 14, 31, 16, 34, 18, 36, 20, 39, 22, 42, 24, 45, 26, 48, 29, 51, 31, 54, 34, 58, 36, 61, 39, 65, 42, 68, 45, 72, 48, 76, 51

Offset

0,5

References

J. H. Conway and N. J. A. Sloane, computed circa 1977.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canadian J. Math. 6, (1954). 274--304. MR0059914 (15,600b).

Index entries for Molien series

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

Formula

G.f.: (1-x+x^2)*(1+x-x^3-x^4-x^5+x^7+x^8)/((1-x)^3*(1+x)^2*(1+x^2)*(1+x+x^2+x^3+x^4)). - Colin Barker, Jan 08 2014

a(n) ~ 1/80*n^2. - Ralf Stephan, Apr 29 2014

a(n) = a(n-2)+a(n-4)+a(n-5)-a(n-6)-a(n-7)-a(n-9)+a(n-11). - Wesley Ivan Hurt, May 24 2021

Maple

(1+x^45)/(1-x^6)/(1-x^12)/(1-x^30):
seq(coeff(series(expand(%), x, 3*n+1), x, 3*n), n=0..100);

Mathematica

CoefficientList[Series[(1-x+x^2)(1+x-x^3-x^4-x^5+x^7+x^8)/((1-x)^3 (1+x)^2 (1+x^2)(1+x+x^2+x^3+x^4), {x, 0, 70}], x]] (* Vincenzo Librandi, Apr 29 2014 *)
LinearRecurrence[{0, 1, 0, 1, 1, -1, -1, 0, -1, 0, 1}, {1, 0, 1, 0, 2, 0, 2, 0, 3, 0, 4}, 100] (* Harvey P. Dale, Aug 29 2016 *)

Prog

(PARI) Vec((x^10-x^5+1)/(-x^11+x^9+x^7+x^6-x^5-x^4-x^2+1) + O(x^100)) \\ Colin Barker, Jan 08 2014
(Magma) R<x>:=PowerSeriesRing(Integers(), 65); Coefficients(R!( (1+x^15)/((1 - x^2)*(1-x^4)*(1-x^10)) )); // G. C. Greubel, Feb 06 2020
(Sage)
def A005868_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x^15)/((1-x^2)*(1-x^4)*(1-x^10)) ).list()
A005868_list(65) # G. C. Greubel, Feb 06 2020

Crossrefs

Sequence in context: A008613 A165685 A035457 * A035455 A029191 A094098

Adjacent sequences: A005865 A005866 A005867 * A005869 A005870 A005871

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved