A008625 G.f.: (1+x^3)*(1+x^5)*(1+x^6)/((1-x^4)*(1-x^6)*(1-x^7)) (or (1+x^5)(1+x^6)/((1-x^3)*(1-x^4)*(1-x^7))).

1, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 10, 10, 11, 13, 13, 14, 16, 17, 18, 20, 21, 22, 24, 25, 27, 29, 30, 32, 34, 35, 37, 40, 41, 43, 46, 47, 49, 52, 54, 56, 59, 61, 63, 66, 68, 71, 74, 76, 79, 82, 84, 87, 91, 93, 96, 100, 102, 105, 109, 112, 115, 119, 122, 125

Offset

0,7

Comments

Poincaré series [or Poincare series] (or Molien series) for mod 2 cohomology of O'Nan group.

Also Poincaré series [or Poincare series] (or Molien series) for mod 2 cohomology of Janko group J_1.

Molien series of 3-dimensional representation of group of order 21 over GF(2).

References

A. Adem and R. J. Milgram, Cohomology of Finite Groups, Springer-Verlag, 2nd. ed., 2004, pp. 77, 95 and 248.

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 106.

Links

Table of n, a(n) for n=0..71.

A. Adem, Recent developments in the cohomology of finite groups, Notices Amer. Math. Soc., 44 (1997), 806-812.

A. Adem and R. J. Milgram, The subgroup structure and mod 2 cohomology of O'Nan's sporadic simple group, J. Algebra 176 (1995), 288-315.

Index entries for Molien series

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

Formula

G.f.: (x^4-x^2+1)*(x^4-x^3+x^2-x+1)/((1-x)*(1-x^3)*(1-x^7)). a(n)=a(n-3)+a(n-7)-a(n-10)+1, n>7.

G.f. can be written as q(x)/((1-x^8)(1-x^12)(1-x^14)) where q is a symmetric polynomial of degree 31 with nonnegative coefficients.

Maple

(1+x^3)*(1+x^5)*(1+x^6)/(1-x^4)/(1-x^6)/(1-x^7);

Mathematica

LinearRecurrence[{1, 0, 1, -1, 0, 0, 1, -1, 0, -1, 1}, {1, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3}, 80] (* Vincenzo Librandi, Jul 19 2015 *)

Prog

(PARI) Vec((1+x^3)*(1+x^5)*(1+x^6)/(1-x^4)/(1-x^6)/(1-x^7) + O(x^80)) \\ Michel Marcus, Jul 18 2015

Crossrefs

Sequence in context: A074286 A025769 A103563 * A029148 A067842 A164066

Adjacent sequences: A008622 A008623 A008624 * A008626 A008627 A008628

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved