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A164548
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Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
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1
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1, 10, 90, 810, 7290, 65610, 590490, 5314365, 47828880, 430456320, 3874074480, 34866378720, 313794784080, 2824129437120, 25416952359660, 228750658083360, 2058738704511840, 18528493377756960, 166755045745830240
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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 A003952, 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)/(36*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
G.f.: (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8). - G. C. Greubel, Jul 17 2021
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MATHEMATICA
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CoefficientList[Series[(1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8), {t, 0, 30}], t] (* or *)
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PROG
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(Magma)
R<t>:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8) )); // G. C. Greubel, Jul 17 2021
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8) ).list()
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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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