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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.
0
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.
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
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved