A165169 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540946432, 2899474070886, 104381066527920, 3757718394142650, 135277862158086480, 4870003036573352160, 175320109276401277440, 6311523932501827576320

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, 35, -630).

Formula

G.f. (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(630*t^8 -

35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 - 35*t^2 - 35*t + 1)