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A165699
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Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.
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3
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1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501434880, 632170063133730, 27815482777840560, 1223881242223068990, 53850774657730746960, 2369434084936444167840, 104255099737040360655360
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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 A170764, 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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FORMULA
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G.f.: (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)/(946*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
G.f.: (1+x)*(1-x^9)/(1 -44*x +989*x^9 -946*x^10). - G. C. Greubel, Apr 26 2019
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1-x^9)/(1-44*x+989*x^9-946*x^10), {x, 0, 20}], x] (* or *) coxG[{9, 946, -43}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)
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PROG
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(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^9)/(1-44*x+989*x^9-946*x^10)) \\ G. C. Greubel, Apr 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^9)/(1-44*x+989*x^9-946*x^10) )); // G. C. Greubel, Apr 26 2019
(Sage) ((1+x)*(1-x^9)/(1-44*x+989*x^9-946*x^10)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019
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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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