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A169315
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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)^30 = I.
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0
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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 30: a(30) = 2821533770084556111179055389204731, A170733(30) = 2821533770084556111179055389204822. - Klaus Brockhaus, Jun 22 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, 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^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*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^30 - 12*t^29 - 12*t^28 - 12*t^27 - 12*t^26 - 12*t^25 - 12*t^24 - 12*t^23 - 12*t^22 - 12*t^21 - 12*t^20 - 12*t^19 - 12*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[29]]+t^30+1, den=Total[-12 t^Range[29]]+78t^18+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Jan 04 2012 *)
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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
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AUTHOR
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STATUS
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approved
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