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

0,7

References

Y. Ito, I. Nakamura, Hilbert schemes and simple singularities, New trends in algebraic geometry (Warwick, 1996), 151-233, Cambridge University Press, 1999.

Links

Table of n, a(n) for n=0..81.

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)

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

Mathematica

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

Prog

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

Crossrefs

Cf. A008651.

Sequence in context: A194292 A308403 A073578 * A061392 A048273 A333535

Adjacent sequences: A087863 A087864 A087865 * A087867 A087868 A087869

Keyword

easy,nonn

Author

Paul Boddington, Oct 27 2003

Extensions

More terms from Benoit Cloitre, Oct 27 2003

Status

approved