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A167078
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Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
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1
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1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414100, 21912208461633931200, 525893003079214176300
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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 A170744, 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 (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).
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FORMULA
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G.f.: (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)/(276*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).
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MATHEMATICA
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CoefficientList[Series[(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)/(276*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 31 2016 *)
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CROSSREFS
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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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