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A164365
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Number of reduced words of length n in Coxeter group on 6 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
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1
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1, 6, 30, 150, 750, 3750, 18750, 93735, 468600, 2342640, 11711400, 58548000, 292695000, 1463250000, 7315125210, 36570003000, 182821904040, 913968987000, 4569142377000, 22842199635000, 114193439625000, 570879418872060
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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 A003948, 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)/(10*t^7 - 4*t^6 - 4*t^5 - 4*t^4 - 4*t^3 - 4*t^2 - 4*t + 1).
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MAPLE
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seq(coeff(series((1+t)*(1-t^7)/(1-5*t+14*t^7-10*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 28 2019
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MATHEMATICA
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CoefficientList[Series[(1+t)*(1-t^7)/(1-5*t+14*t^7-10*t^8), {t, 0, 30}], t] (* G. C. Greubel, Sep 15 2017 *)
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PROG
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(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^7)/(1-5*t+14*t^7-10*t^8)) \\ G. C. Greubel, Sep 15 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^7)/(1-5*t+14*t^7-10*t^8) )); // G. C. Greubel, Aug 28 2019
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^7)/(1-5*t+14*t^7-10*t^8)).list()
(GAP) a:=[6, 30, 150, 750, 3750, 18750, 93735];; for n in [8..30] do a[n]:=4*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -10*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Aug 28 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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