A165184 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26238, 78696, 236040, 707976, 2123496, 6369192, 19103688, 57299400, 171863208, 515484678, 1546139268, 4637473692, 13909589316, 41720274396, 125135347716, 375329632284, 1125759710916

Offset

0,2

Comments

The initial terms coincide with those of A003946, 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..25.

Index entries for linear recurrences with constant coefficients, signature (2, 2, 2, 2, 2, 2, 2, 2, -3).

Formula

G.f. (t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t +

1)/(3*t^9 - 2*t^8 - 2*t^7 - 2*t^6 - 2*t^5 - 2*t^4 - 2*t^3 - 2*t^2 - 2*t

+ 1)

Mathematica

coxG[{9, 3, -2, 30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 11 2017 *)

Crossrefs

Sequence in context: A164353 A347506 A164697 * A165756 A166328 A166468

Adjacent sequences: A165181 A165182 A165183 * A165185 A165186 A165187

Keyword

nonn

Author

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

Status

approved