A165213 Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 6, 30, 150, 750, 3750, 18750, 93750, 468750, 2343735, 11718600, 58592640, 292961400, 1464798000, 7323945000, 36619500000, 183096375000, 915476250000, 4577353125210, 22886625003000, 114432421904040, 572158593987000

Offset

0,2

Comments

The initial terms coincide with those of A003948, 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..21.

Index entries for linear recurrences with constant coefficients, signature (4, 4, 4, 4, 4, 4, 4, 4, -10).

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)/(10*t^9 - 4*t^8 - 4*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t

+ 1)

Mathematica

With[{num=Total[2t^Range[8]]+t^9+1, den=Total[-4 t^Range[8]]+10t^9+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jan 22 2012 *)

Crossrefs

Sequence in context: A163922 A164365 A164741 * A165777 A166364 A166500

Adjacent sequences: A165210 A165211 A165212 * A165214 A165215 A165216

Keyword

nonn

Author

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

Status

approved