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A166682
Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
1
1, 34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910946, 1449027061218, 47817893020194, 1577990469666402, 52073685498991266, 1718431621466711217, 56708243508401451648, 1871372035777247294016, 61755277180649140560384
OFFSET
0,2
COMMENTS
The initial terms coincide with those of A170753, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
LINKS
Index entries for linear recurrences with constant coefficients, signature (32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, -528).
FORMULA
G.f.: (t^12 + 2*t^11 + 2*t^10 + 2*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)/(528*t^12 - 32*t^11 - 32*t^10 - 32*t^9 - 32*t^8 - 32*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
MATHEMATICA
With[{num=Total[2t^Range[11]]+t^12+1, den=Total[-32 t^Range[11]]+528t^12+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Aug 19 2011 *)
CROSSREFS
Sequence in context: A165649 A166130 A166428 * A167087 A167396 A167785
KEYWORD
nonn
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved