A164673 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540945766, 2899474023600, 104381063987130, 3757718272487760, 135277856691798240, 4870002800665336320, 175320099375333696000, 6311523525361750684170

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170756, 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 (35,35,35,35,35,35,-630).

Programs

Mathematica

coxG[{7,630,-35}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 15 2020 *)

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(630*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).