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A164667
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Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
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2
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1, 31, 930, 27900, 837000, 25110000, 753300000, 22598999535, 677969972100, 20339098744965, 610172949807900, 18305188118005500, 549155632253220000, 16474668628988250000, 494240048711397215760, 14827201156594414216125
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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 A170750, 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^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).
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MAPLE
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seq(coeff(series((1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Sep 15 2019
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MATHEMATICA
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CoefficientList[Series[(1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2019 *)
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PROG
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(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8)) \\ G. C. Greubel, Sep 15 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8) )); // G. C. Greubel, Sep 15 2019
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8)).list()
(GAP) a:=[31, 930, 27900, 837000, 25110000, 753300000, 22598999535];; for n in [8..20] do a[n]:=29*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -435*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 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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