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A008625
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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))).
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| Poincare series (or Molien series) for mod 2 cohomology of O'Nan group.
Also 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).
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REFERENCES
| 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.
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.
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LINKS
| Index entries for Molien series
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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.
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MAPLE
| (1+x^3)*(1+x^5)*(1+x^6)/(1-x^4)/(1-x^6)/(1-x^7);
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CROSSREFS
| Sequence in context: A074286 A025769 A103563 * A029148 A067842 A164066
Adjacent sequences: A008622 A008623 A008624 * A008626 A008627 A008628
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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