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A163749
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Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
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1
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1, 45, 1980, 87120, 3833280, 168663330, 7421142960, 326528374590, 14367164193360, 632151515809440, 27814503513864870, 1223830974655177020, 53848246968666559530, 2369308966391783748420, 104248982914726676312880
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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 A170764, 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^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
a(n) = 43*a(n-1)+43*a(n-2)+43*a(n-3)+43*a(n-4)-946*a(n-5). - Wesley Ivan Hurt, May 11 2021
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MAPLE
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seq(coeff(series((1+t)*(1-t^5)/(1-44*t+989*t^5-946*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019
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MATHEMATICA
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CoefficientList[Series[(1+t)*(1-t^5)/(1-44*t+989*t^5-946*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 02 2017 *)
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PROG
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(PARI) my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-44*t+989*t^5-946*t^6)) \\ G. C. Greubel, Aug 02 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6) )); // G. C. Greubel, Aug 09 2019
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^5)/(1-43*t+945*t^5-903*t^6)).list()
(GAP) a:=[45, 1980, 87120, 3833280, 168663330];; for n in [6..30] do a[n]:=43*(a[n-1]+a[n-2]+a[n-3]+a[n-4]) -946*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, Aug 09 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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