A091971 - OEIS

A091971

G.f.: (1+x^3)*(1+x^5)*(1+x^6)/((1-x^4)*(1-x^5)*(1-x^6)).

1, 0, 0, 1, 1, 2, 2, 1, 3, 4, 4, 5, 5, 6, 8, 9, 9, 10, 12, 13, 15, 16, 16, 19, 21, 22, 24, 25, 27, 30, 32, 33, 35, 38, 40, 43, 45, 46, 50, 53, 55, 58, 60, 63, 67, 70, 72, 75, 79, 82, 86, 89, 91, 96, 100, 103, 107, 110, 114, 119, 123, 126, 130, 135, 139, 144, 148, 151, 157, 162, 166

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OFFSET

0,6

COMMENTS

Let G = G_2(q) or ^3D_4(q) with q == 1 mod 4. The Poincaré series [or Poincare series] (or Molien series) for G is independent of q and is given here.

REFERENCES

A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004; p. 242.

LINKS

Table of n, a(n) for n=0..70.

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

FORMULA

G.f.: -(x^4-x^3+x^2-x+1)*(x^4-x^2+1) / ( (1+x+x^2)*(x^4+x^3+x^2+x+1)*(x-1)^3 ). - R. J. Mathar, Sep 27 2014

MATHEMATICA

CoefficientList[Series[(1+x^3)*(1+x^5)*(1+x^6)/((1-x^4)*(1-x^5)*(1-x^6)), {x, 0, 80}], x] (* or *) LinearRecurrence[{1, 0, 1, -1, 1, -1, 0, -1, 1}, {1, 0, 0, 1, 1, 2, 2, 1, 3}, 80] (* Harvey P. Dale, Feb 19 2017 *)

CROSSREFS

Sequence in context: A276325 A286548 A256134 * A341096 A065185 A289412

Adjacent sequences: A091968 A091969 A091970 * A091972 A091973 A091974

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 15 2004

STATUS

approved