

A087866


Composition length of the nth 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, 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
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OFFSET

0,7


REFERENCES

Y. Ito, I. Nakamura, Hilbert schemes and simple singularities, New trends in algebraic geometry (Warwick, 1996), 151233, 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.: (1x^15)/((1x)*(1x^6)*(1x^10)).
a(n) = n/60*(15+(1)^n+b(n)) where b(n) is the 30periodic 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[(1x^15)/((1x)(1x^6)(1x^10)), {x, 0, 100}], x] (* Harvey P. Dale, Jan 20 2019 *)


PROG

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


CROSSREFS

Cf. A008651.
Sequence in context: A194292 A308403 A073578 * A061392 A048273 A175387
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



