A164631 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 19, 342, 6156, 110808, 1994544, 35901792, 646232085, 11632174452, 209379084903, 3768822534060, 67838787717588, 1221097856797728, 21979755624219696, 395635496869474254, 7121437065054388737

Offset: 0

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Keywords

• nonn

Comments

The initial terms coincide with those of A170738, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

• Index entries for linear recurrences with constant coefficients, signature (17,17,17,17,17,17,-153).

Programs

Mathematica

coxG[{7,153,-17}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 27 2017 *)

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).