A162925 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 5, 20, 80, 310, 1200, 4650, 18000, 69690, 269820, 1044630, 4044420, 15658470, 60623640, 234711810, 908715240, 3518201250, 13621143060, 52735907790, 204173464860, 790482339630, 3060448278480, 11848896802170, 45874441471680

Offset: 0

Author

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

Keywords

• nonn

Comments

The initial terms coincide with those of A003947, 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 (3, 3, 3, -6).

Programs

Mathematica

coxG[{4,6,-3,30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 28 2023 *)

Formula

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