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A087504
Composition length of the n-th symmetric power of the natural representation of a finite subgroup of SL(2,C) of type E_7 (binary octahedral group).
2
1, 1, 1, 1, 2, 2, 3, 3, 4, 3, 4, 4, 6, 5, 6, 5, 7, 6, 8, 7, 9, 7, 9, 8, 11, 9, 11, 9, 12, 10, 13, 11, 14, 11, 14, 12, 16, 13, 16, 13, 17, 14, 18, 15, 19, 15, 19, 16, 21, 17, 21, 17, 22, 18, 23, 19, 24, 19, 24, 20, 26, 21, 26, 21, 27, 22, 28, 23, 29, 23, 29, 24
OFFSET
0,5
REFERENCES
Y. Ito, I. Nakamura, Hilbert schemes and simple singularities, New trends in algebraic geometry (Warwick, 1996), 151-233, Cambridge University Press, 1999.
LINKS
FORMULA
G.f.: (1-x^9)/((1-x)(1-x^4)(1-x^6)).
a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=2, a(5)=2, a(6)=3, a(7)=3, a(n)= a(n-1)- a(n-3)+2*a(n-4)-a(n-5)+a(n-7)-a(n-8). [Harvey P. Dale, May 09 2012]
MATHEMATICA
CoefficientList[Series[(1-x^9)/((1-x)(1-x^4)(1-x^6)), {x, 0, 30}], x] (* or *) LinearRecurrence[{1, 0, -1, 2, -1, 0, 1, -1}, {1, 1, 1, 1, 2, 2, 3, 3}, 31] (* Harvey P. Dale, May 09 2012 *)
PROG
(PARI) Vec((1-x^9)/((1-x)*(1-x^4)*(1-x^6)) + O(x^80)) \\ Michel Marcus, Aug 19 2015
CROSSREFS
Cf. A008647.
Sequence in context: A356874 A057022 A287896 * A067539 A166312 A138099
KEYWORD
easy,nonn
AUTHOR
Paul Boddington, Oct 23 2003
EXTENSIONS
More terms from Michel Marcus, Aug 19 2015
STATUS
approved