A165131 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651056, 27292513167360, 846067907712000, 26228105124311040, 813071258396052480, 25205208996092344320, 781361478439118914560, 24222205817980629811200

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A170751, 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 (30, 30, 30, 30, 30, 30, 30, -465).

Programs

Mathematica

coxG[{8,465,-30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 03 2023 *)

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)/(465*t^8 -

30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1)