A091423 G.f.: ((1 + x^9)*(1 + x^(15)) ) / ( (1 - x^3)*(1 - x^5)*(1 - x^8)*(1 - x^(12))).

1, 0, 0, 1, 0, 1, 1, 0, 2, 2, 1, 2, 3, 2, 3, 5, 3, 5, 6, 4, 8, 8, 6, 10, 12, 10, 12, 15, 13, 17, 19, 16, 23, 24, 21, 28, 30, 28, 33, 37, 36, 41, 44, 42, 51, 54, 50, 60, 65, 62, 70, 75, 74, 83, 87, 86, 98, 102, 99, 112, 119, 116, 127, 135, 135, 147, 152, 152, 168, 174, 172, 188, 198, 196

Offset

0,9

Comments

Poincaré series [or Poincare series] (or Molien series) for F_2[x_1..x_4]^(A_6).

References

A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004, last page of Chapter III.

Links

Table of n, a(n) for n=0..73.

Index entries for linear recurrences with constant coefficients, signature (1, -1, 3, -3, 4, -6, 6, -7, 9, -9, 9, -10, 9, -9, 9, -7, 6, -6, 4, -3, 3, -1, 1, -1).

Formula

G.f.: (1-x+x^2) *(x^4-x^3+x^2-x+1) *(x^6-x^3+1) *(x^8+x^7-x^5-x^4-x^3+x+1) / ( (x^4+x^3+x^2+x+1) *(x^4-x^2+1) *(x^4+1) *(x^2+1)^2 *(1+x+x^2)^2 *(x-1)^4 ). - R. J. Mathar, Dec 18 2014

Mathematica

CoefficientList[Series[((1+x^9)(1+x^(15)))/((1-x^3)(1-x^5)(1-x^8)(1-x^(12))), {x, 0, 80}], x] (* or *) LinearRecurrence[{1, -1, 3, -3, 4, -6, 6, -7, 9, -9, 9, -10, 9, -9, 9, -7, 6, -6, 4, -3, 3, -1, 1, -1}, {1, 0, 0, 1, 0, 1, 1, 0, 2, 2, 1, 2, 3, 2, 3, 5, 3, 5, 6, 4, 8, 8, 6, 10}, 80] (* Harvey P. Dale, Dec 27 2023 *)

Prog

(PARI) Vec(((1 + x^9)*(1 + x^(15)))/((1 - x^3)*(1 - x^5)*(1 - x^8)*(1 - x^(12))) + O(x^80)) \\ Jinyuan Wang, Mar 10 2020

Crossrefs

Sequence in context: A333529 A369363 A022872 * A221914 A264401 A173304

Adjacent sequences: A091420 A091421 A091422 * A091424 A091425 A091426

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 16 2004

Status

approved