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A166128
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Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
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1
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1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909140976, 26228105183354880, 813071260683525120, 25205209081174517760, 781361481515952460800, 24222205926980341002240
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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 A170751, 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 (30, 30, 30, 30, 30, 30, 30, 30, 30, -465).
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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)/(465*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
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MAPLE
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seq(coeff(series((1+t)*(1-t^10)/(1 -31*t +495*t^10 -465*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Mar 11 2020
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MATHEMATICA
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CoefficientList[Series[(1+t)*(1-t^10)/(1 -31*t +495*t^10 -465*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 26 2016 *)
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PROG
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(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^10)/(1 -31*t +495*t^10 -465*t^11) ).list() A166128_list(30) # G. C. Greubel, Mar 11 2020
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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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