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).
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
References
- Y. Ito, I. Nakamura, Hilbert schemes and simple singularities, New trends in algebraic geometry (Warwick, 1996), 151-233, Cambridge University Press, 1999.
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1, 0, -1, 2, -1, 0, 1, -1).
Crossrefs
Cf. A008647.
Programs
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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 *) -
PARI
Vec((1-x^9)/((1-x)*(1-x^4)*(1-x^6)) + O(x^80)) \\ Michel Marcus, Aug 19 2015
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]
Extensions
More terms from Michel Marcus, Aug 19 2015