A087866 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).

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

Offset: 0

Author

Paul Boddington, Oct 27 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

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,1,-1,0,0,1,-1,0,0,0,0,-1,1)

Crossrefs

Cf. A008651.

Programs

Mathematica

CoefficientList[Series[(1-x^15)/((1-x)(1-x^6)(1-x^10)),{x,0,100}],x] (* Harvey P. Dale, Jan 20 2019 *)

PARI

a(n)=polcoeff((1-x^15)/((1-x)*(1-x^6)*(1-x^10))+O(x^(n+1)),n)

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, Oct 27 2003

Extensions

More terms from Benoit Cloitre, Oct 27 2003