

A008625


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


0



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
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OFFSET

0,7


COMMENTS

PoincarĂ© series [or Poincare series] (or Molien series) for mod 2 cohomology of O'Nan group.
Also PoincarĂ© series [or Poincare series] (or Molien series) for mod 2 cohomology of Janko group J_1.
Molien series of 3dimensional representation of group of order 21 over GF(2).


REFERENCES

A. Adem and R. J. Milgram, Cohomology of Finite Groups, SpringerVerlag, 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), 806812.
A. Adem and R. J. Milgram, The subgroup structure and mod 2 cohomology of O'Nan's sporadic simple group, J. Algebra 176 (1995), 288315.
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^4x^2+1)*(x^4x^3+x^2x+1)/((1x)*(1x^3)*(1x^7)). a(n)=a(n3)+a(n7)a(n10)+1, n>7.
G.f. can be written as q(x)/((1x^8)(1x^12)(1x^14)) where q is a symmetric polynomial of degree 31 with nonnegative coefficients.


MAPLE

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



