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A168739
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Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.
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1
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1, 14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991222, 1930018885886, 25090245516518, 326173191714734, 4240251492291542, 55123269399790046, 716602502197270598
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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 A170733, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 121105822871338730971, A170733(18) = 121105822871338731062. - Klaus Brockhaus, Mar 27 2011
Computed with MAGMA using commands similar to those used to compute A154638.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).
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FORMULA
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G.f.: (t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*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)/(78*t^18 - 12*t^17 - 12*t^16 - 12*t^15 - 12*t^14 - 12*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).
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MATHEMATICA
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With[{num=Total[2t^Range[17]]+t^18+1, den=Total[-12 t^Range[17]]+ 78t^18+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Jun 27 2011 *)
CoefficientList[Series[(t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*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)/(78*t^18 - 12*t^17 - 12*t^16 - 12*t^15 - 12*t^14 - 12*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1), {t, 0, 500}], t] (* G. C. Greubel, Aug 08 2016 *)
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CROSSREFS
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Cf. A170733 (G.f.: (1+x)/(1-13*x)).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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