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A165876
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Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
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1
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1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093749880, 9226406246400, 138396093669120, 2075941404633600, 31139121063456000, 467086815861120000, 7006302236556000000
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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 A170735, 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 (14,14,14,14,14,14,14,14,14,-105).
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FORMULA
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G.f.: (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)/(105*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).
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MAPLE
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seq(coeff(series((1+t)*(1-t^10)/(1-15*t+129*t^10-105*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 23 2019
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MATHEMATICA
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CoefficientList[Series[(1+t)*(1-t^10)/(1-15*t+129*t^10-105*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 17 2016 *)
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PROG
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(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-15*t+129*t^10-105*t^11)) \\ G. C. Greubel, Aug 07 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-15*t+129*t^10-105*t^11) )); // G. C. Greubel, Aug 10 2019
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-15*t+129*t^10-105*t^11)).list()
(GAP) a:=[16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093749880];; for n in [11..20] do a[n]:=14*Sum([1..9], j-> a[n-j]) -105*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 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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