A087866 - OEIS

%I #15 Jul 23 2019 08:17:29

%S 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,

%T 9,8,10,9,10,9,11,10,12,11,12,10,12,11,13,12,14,12,14,13,15,13,15,13,

%U 15,14,17,15,17,15,17,15,18,16,18,16,19,17,20,18,20,17,20,18,21,19,22,19

%N 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).

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

%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1,0,0,1,-1,0,0,0,0,-1,1)

%F G.f.: (1-x^15)/((1-x)*(1-x^6)*(1-x^10)).

%F 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

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

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

%Y Cf. A008651.

%K easy,nonn

%O 0,7

%A _Paul Boddington_, Oct 27 2003

%E More terms from _Benoit Cloitre_, Oct 27 2003