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A166327
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Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
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1
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1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3069, 6132, 12255, 24492, 48948, 97824, 195504, 390720, 780864, 1560576, 3118848, 6233094, 12456993, 24895608, 49754487, 99435570, 198724440, 397155696, 793725456, 1586279904, 3170219520
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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 A003945, 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 (2,-1,2,-1,2,-1,2,-1,2,-1).
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FORMULA
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G.f.: (t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1) / (t^10 - 2*t^9 + t^8 - 2*t^7 + t^6 - 2*t^5 + t^4 - 2*t^3 + t^2 - 2*t + 1).
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MAPLE
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seq(coeff(series((1+t)*(1-t^11)/(1-2*t+2*t^11-t^12), t, n+1), t, n), n = 0..30); # G. C. Greubel, Mar 12 2020
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MATHEMATICA
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CoefficientList[Series[(1+t)*(1-t^11)/(1-2*t+2*t^11-t^12), {t, 0, 30}], t] (* G. C. Greubel, May 09 2016 *)
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PROG
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(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^11)/(1-2*t+2*t^11-t^12) ).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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