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

Author

Paul Boddington, Oct 23 2003

Keywords

• easy
• nonn

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

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