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A167105
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Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.
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1
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1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236196, 708588, 2125764, 6377286, 19131840, 57395472, 172186272, 516558384, 1549673856, 4649017680, 13947041376, 41841089136, 125523162432, 376569172368, 1129706572320
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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 A003946, 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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Index entries for linear recurrences with constant coefficients, signature (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -3).
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FORMULA
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G.f.: (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)/(3*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).
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MATHEMATICA
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CoefficientList[Series[(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) / (3*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), {t, 0, 50}], t] (* G. C. Greubel, Jun 03 2016 *)
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CROSSREFS
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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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