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A166857
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Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.
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1
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1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12285, 24564, 49119, 98220, 196404, 392736, 785328, 1570368, 3140160, 6279168, 12556032, 25107456, 50205696, 100392966, 200749089, 401424504, 802701687, 1605108786, 3209628504
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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 A003945, 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, -1, 2, -1, 2, -1, 2, -1, 2, -1, 2, -1).
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FORMULA
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G.f.: (t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)/(t^12 - 2*t^11 + t^10 - 2*t^9 + t^8 - 2*t^7 + t^6 - 2*t^5 + t^4 - 2*t^3 + t^2 - 2*t + 1).
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MATHEMATICA
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CoefficientList[Series[(t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)/(t^12 - 2*t^11 + t^10 - 2*t^9 + t^8 - 2*t^7 + t^6 - 2*t^5 + t^4 - 2*t^3 + t^2 - 2*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 25 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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