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A008613
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Molien series for 3-dimensional representation of A_5.
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1
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1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 3, 0, 4, 0, 4, 1, 5, 1, 6, 1, 7, 2, 8, 2, 9, 3, 10, 4, 11, 4, 13, 5, 14, 6, 15, 7, 17, 8, 18, 9, 20, 10, 22, 11, 23, 13, 25, 14, 27, 15, 29, 17, 31, 18, 33, 20, 35, 22, 37, 23, 40, 25, 42, 27
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| Also arises in connection with Lee weight enumerators of codes over GF(5).
Partitions of n into (any number of) parts 2, 6, and 10, and at most one part 15. [Joerg Arndt, May 15 2011]
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REFERENCES
| D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 101.
H. Derksen and G. Kemper, Computational Invariant Theory, Springer, 2002; p. 92.
G. van der Geer, Hilbert Modular Surfaces, Springer-Verlag, 1988; p. 192.
F. Klein, Lectures on the Icosahedron ..., 2nd Rev. Ed., 1913; reprinted by Dover, NY, 1956; see pp. 236-243.
F. Klein, Werke, II, p. 354.
J. S. Leon, V. S. Pless and N. J. A. Sloane, Self-dual codes over GF(5), J. Combin. Theory, A 32 (1982), 178-194.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
F. J. MacWilliams, C. L. Mallows and N. J. A. Sloane, Generalizations of Gleason's theorem on weight enumerators of self-dual codes, IEEE Trans. Inform. Theory, 18 (1972), 794-805; see p. 802, col. 2, foot.
Index entries for Molien series
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FORMULA
| G.f.: (1+x^15)/((1-x^2)*(1-x^6)*(1-x^10)).
a(0)=1, a(1)=0, a(2)=1, a(3)=0, a(4)=1, a(5)=0, a(6)=2, a(7)=0, a(8)=2, a(9)=0, a(10)=3, a(n)=-a(n-1)+a(n-2)+2*a(n-3)+a(n-4)-a(n-7)-2*a(n-8)-a(n-9)+a(n-10)+a (n-11) [From Harvey P. Dale, May 15 2011]
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MAPLE
| (1+x^15)/((1-x^2)*(1-x^6)*(1-x^10));
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MATHEMATICA
| CoefficientList[Series[(1+x^15)/((1-x^2)(1-x^6)(1-x^10)), {x, 0, 100}], x] (* or *) LinearRecurrence[{-1, 1, 2, 1, 0, 0, -1, -2, -1, 1, 1}, {1, 0, 1, 0, 1, 0, 2, 0, 2, 0, 3}, 100] (* From Harvey P. Dale, May 15 2011 *)
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CROSSREFS
| Sequence in context: A025805 A029192 A128619 * A165685 A035457 A005868
Adjacent sequences: A008610 A008611 A008612 * A008614 A008615 A008616
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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