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A164696
Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.
0
1, 3, 6, 12, 24, 48, 96, 192, 381, 756, 1503, 2988, 5940, 11808, 23472, 46656, 92742, 184353, 366456, 728439, 1447986, 2878296, 5721456, 11373072, 22607316, 44938668, 89328777, 177567132, 352966731, 701624856, 1394685096, 2772345504
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A003945, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
FORMULA
G.f.: (t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(t^8 - t^7 - t^6 - t^5 - t^4 - t^3 - t^2 - t + 1).
MATHEMATICA
With[{num=Total[2t^Range[7]]+t^8+1, den=Total[-t^Range[7]]+t^8+1}, CoefficientList[ Series[ num/den, {t, 0, 40}], t]] (* Harvey P. Dale, Aug 05 2011 *)
CROSSREFS
Sequence in context: A115829 A115805 A356040 * A344040 A165183 A046944
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved