A162493 Number of reduced words of length n in the Weyl group E_7 on 7 generators and order 2903040.

1, 7, 27, 77, 182, 378, 713, 1247, 2051, 3205, 4795, 6909, 9632, 13040, 17194, 22134, 27874, 34398, 41657, 49567, 58009, 66831, 75852, 84868, 93659, 101997, 109655, 116417, 122087, 126497, 129514, 131046, 131046, 129514, 126497, 122087, 116417, 109655

Offset

0,2

References

N. Bourbaki, Groupes et alg. de Lie, Chap. 4, 5, 6. (The group is defined in Planche VI.)

H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, Table 10.

J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See under Poincaré polynomial.

Links

Jinyuan Wang, Table of n, a(n) for n = 0..63

Formula

G.f.: (1-x^2)*(1-x^6)*(1-x^8)*(1-x^10)*(1-x^12)*(1-x^14)*(1-x^18)/(1-x)^7.

Prog

(Magma) G := CoxeterGroup(GrpFPCox, "E7");
f := GrowthFunction(G);
Coefficients(f);
(PARI) Vec((1-x^2)*(1-x^6)*(1-x^8)*(1-x^10)*(1-x^12)*(1-x^14)*(1-x^18)/(1-x)^7 + O(x^64)) \\ Jinyuan Wang, Mar 08 2020

Crossrefs

Cf. A161409, A162494.

Sequence in context: A162210 A161716 A374930 * A005585 A161410 A267169

Adjacent sequences: A162490 A162491 A162492 * A162494 A162495 A162496

Keyword

nonn,fini,full

Author

John Cannon and N. J. A. Sloane, Dec 01 2009

Status

approved