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A163219
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Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
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1
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1, 36, 1260, 44100, 1542870, 53978400, 1888472880, 66069561600, 2311490430270, 80869130653500, 2829263840578980, 98983800307381500, 3463018394666864670, 121156152466965222600, 4238733846520797445080, 148295107229819712107400
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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 A170755, 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^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(595*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
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MATHEMATICA
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CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(595*t^4-34*t^3-34*t^2 - 34*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[{34, 34, 34, -595}, {36, 1260, 44100, 1542870}, 20]] (* G. C. Greubel, Dec 11 2016 *)
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PROG
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(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(595*t^4-34*t^3 - 34*t^2-34*t+1)) \\ G. C. Greubel, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-35*x+629*x^4-595*x^5) )); // G. C. Greubel, Apr 30 2019
(Sage) ((1+x)*(1-x^4)/(1-35*x+629*x^4-595*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019
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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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