A162847 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

1, 35, 1190, 39865, 1335180, 44708895, 1497090210, 50130334485, 1678623324840, 56209003149915, 1882168556020830, 63024751767399345, 2110395119905763460, 70666959205286686935, 2366295806989839830490, 79235839622172041773965

Offset

0,2

Comments

The initial terms coincide with those of A170754, 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..15.

Index entries for linear recurrences with constant coefficients, signature (33, 33, -561).

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(561*t^3 - 33*t^2 - 33*t + 1).

a(n) = 33*a(n-1) + 33*a(n-2) - 561*a(n-3). - Wesley Ivan Hurt, Apr 20 2021

Mathematica

coxG[{3, 561, -33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 05 2016 *)

Crossrefs

Sequence in context: A306685 A046176 A352183 * A029546 A305539 A163218

Adjacent sequences: A162844 A162845 A162846 * A162848 A162849 A162850

Keyword

nonn

Author

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

Status

approved