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A165654
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Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.
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0
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1, 37, 1332, 47952, 1726272, 62145792, 2237248512, 80540946432, 2899474071552, 104381066575206, 3757718396683440, 135277862279741370, 4870003042039640400, 175320109512309293280, 6311523942402895157760
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OFFSET
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0,2
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COMMENTS
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The initial terms coincide with those of A170756, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
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LINKS
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Table of n, a(n) for n=0..14.
Index entries for linear recurrences with constant coefficients, signature (35, 35, 35, 35, 35, 35, 35, 35, -630).
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FORMULA
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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)/(630*t^9 - 35*t^8 - 35*t^7 - 35*t^6 - 35*t^5 - 35*t^4 - 35*t^3 -
35*t^2 - 35*t + 1)
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MATHEMATICA
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With[{num=Total[2t^Range[8]]+t^9+1, den=Total[-35 t^Range[8]]+ 630t^9+1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Nov 01 2011 *)
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CROSSREFS
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Sequence in context: A164070 A164673 A165169 * A166167 A166431 A166689
Adjacent sequences: A165651 A165652 A165653 * A165655 A165656 A165657
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KEYWORD
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nonn
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AUTHOR
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John Cannon and N. J. A. Sloane, Dec 03 2009
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STATUS
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approved
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