A089010 a(n) = 1 if n is an exponent of the Weyl group W(E_8), 0 otherwise.

1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Paul Boddington, Nov 03 2003

Keywords

• easy
• nonn

Comments

The exponents are 1, 7, 11, 13, 17, 19, 23, 29. The point of this sequence is that a similar generating function gives the exponents for any finite Coxeter group.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for characteristic functions

Crossrefs

Cf. A005776, A089011.

Programs

Mathematica

PadRight[CoefficientList[Series[x(1-x^20)(1-x^24)/((1-x^6)(1-x^10)),{x,0,120}],x],120,0] (* Harvey P. Dale, May 15 2018 *)

PARI

Vec(x*(1-x^20)*(1-x^24)/((1-x^6)*(1-x^10)) + O(x^90)) \\ Michel Marcus, Aug 19 2015

Formula

G.f.: x*(1-x^20)*(1-x^24)/((1-x^6)*(1-x^10)).