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

0,2

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

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (3, 3, 3, -6).

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)

Mathematica

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

Crossrefs

Sequence in context: A117422 A154639 A214939 * A163316 A163878 A164354

Adjacent sequences: A162922 A162923 A162924 * A162926 A162927 A162928

Keyword

nonn

Author

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

Status

approved