A008626 Poincaré series [or Poincare series] (or Molien series) for H*(M_11, GF(3)) and H*(M_23, GF(3)).

1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 1, 0, 0, 2, 2, 0, 1, 2, 1, 0, 1, 3, 2, 0, 2, 4, 2, 0, 1, 4, 3, 0, 2, 4, 2, 0, 2, 5, 3, 0, 3, 6, 3, 0, 2, 6, 4, 0, 3, 6, 3, 0, 3, 7, 4, 0, 4, 8, 4, 0, 3, 8, 5, 0, 4, 8, 4, 0, 4, 9, 5, 0, 5, 10, 5, 0, 4, 10, 6, 0, 5, 10, 5, 0, 5, 11, 6, 0, 6, 12, 6, 0, 5, 12, 7, 0, 6, 12, 6, 0

Offset

0,12

References

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 107.

Links

Table of n, a(n) for n=0..101.

Index entries for linear recurrences with constant coefficients, signature (2,-3,4,-4,4,-4,4,-4,4,-4,4,-4,4,-4,4,-3,2,-1).

Formula

G.f.: ( 1 -3*x^7 +3*x^8 -2*x^15 +x^16-2*x -3*x^9 +3*x^2 +3*x^14 -4*x^3 +4*x^4 -4*x^5 +4*x^6 +4*x^10 -4*x^11 +4*x^12 -4*x^13 ) / ( (1+x^4)*(x^8+1)*(x-1)^2*(x^2+1)^2 ). - R. J. Mathar, Dec 18 2014

Maple

1/2*((1+x^3)*(1+x^4)*(1+x^7)*(1+x^8)+(1-x^3)*(1-x^4)*(1-x^7)*(1-x^8))/(1-x^8)/(1-x^16)

Mathematica

LinearRecurrence[{2, -3, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -4, 4, -3, 2, -1}, {1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 1, 0, 0, 2, 2, 0}, 102]
(* Ray Chandler, Jul 15 2015 *)

Crossrefs

Sequence in context: A281081 A103344 A123484 * A058626 A258278 A122856

Adjacent sequences: A008623 A008624 A008625 * A008627 A008628 A008629

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved