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A087866
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Composition length of the n-th symmetric power of the natural representation of a finite subgroup of SL(2,C) of type E_8 (binary icosahedral group).
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1
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1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 3, 4, 4, 5, 5, 6, 5, 6, 6, 7, 6, 7, 6, 7, 7, 9, 8, 9, 8, 9, 8, 10, 9, 10, 9, 11, 10, 12, 11, 12, 10, 12, 11, 13, 12, 14, 12, 14, 13, 15, 13, 15, 13, 15, 14, 17, 15, 17, 15, 17, 15, 18, 16, 18, 16, 19, 17, 20, 18, 20, 17, 20, 18, 21, 19, 22, 19
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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REFERENCES
| Y. Ito, I. Nakamura, Hilbert schemes and simple singularities, New trends in algebraic geometry (Warwick, 1996), 151-233, Cambridge University Press, 1999.
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FORMULA
| G.f.: (1-x^15)/((1-x)*(1-x^6)*(1-x^10)).
a(n)=n/60*(15+(-1)^n+b(n)) where b(n) is the 30-periodic sequence {60, 46, 28, 18, -4, -10, 24, 22, -8, -6, 20, 26, 48, 58, 16, -30, -16, 2, 12, 34, 40, 6, 8, 38, 36, 10, 4, -18, -28, 14} - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 27 2003
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PROG
| (PARI) a(n)=polcoeff((1-x^15)/((1-x)*(1-x^6)*(1-x^10))+O(x^(n+1)), n)
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CROSSREFS
| Cf. A008651.
Sequence in context: A064658 A194292 A073578 * A061392 A048273 A175387
Adjacent sequences: A087863 A087864 A087865 * A087867 A087868 A087869
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Boddington (psb(AT)maths.warwick.ac.uk), Oct 27 2003
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 27 2003
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