A089012 a(n) = 1 if n is an exponent of the Weyl group W(E_6), 0 otherwise.

1, 0, 0, 1, 1, 0, 1, 1, 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, 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, 4, 5, 7, 8, 11. 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..1001
• Index entries for characteristic functions

Crossrefs

Characteristic function of A005556.

Programs

Mathematica

CoefficientList[Series[(1 - x^8) (1 - x^9)/((1 - x^3) (1 - x^4)), {x, 0, 11}], x] (* Michael De Vlieger, Oct 10 2017 *)

Scheme

(define (A089012 n) (if (member n '(1 4 5 7 8 11)) 1 0)) ;; Antti Karttunen, Oct 10 2017

Formula

G.f.: (1-x^8)*(1-x^9)/((1-x^3)*(1-x^4)).

Extensions

More zeros from Antti Karttunen, Oct 10 2017