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A164353
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Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
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1
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1, 4, 12, 36, 108, 324, 972, 2910, 8712, 26088, 78120, 233928, 700488, 2097576, 6281094, 18808452, 56321052, 168650820, 505017180, 1512250884, 4528366236, 13559985966, 40604758920, 121589096856, 364092999624, 1090259865432
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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 A003946, 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.: (x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1)/(3*x^7 - 2*x^6 - 2*x^5 - 2*x^4 - 2*x^3 - 2*x^2 - 2*x + 1).
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MAPLE
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seq(coeff(series((1+t)*(1-t^7)/(1-3*t+5*t^7-3*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 24 2019
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MATHEMATICA
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CoefficientList[Series[(x^7 + 2 x^6 + 2 x^5 + 2 x^4 + 2 x^3 + 2 x^2 + 2 x + 1)/(3 x^7 - 2 x^6 - 2 x^5 - 2 x^4 - 2 x^3 - 2 x^2 - 2 x + 1), {x, 0, 40}], x ] (* Vincenzo Librandi, Apr 29 2014 *)
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PROG
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(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^7)/(1-3*t+5*t^7-3*t^8)) \\ G. C. Greubel, Sep 15 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^7)/(1-3*t+5*t^7-3*t^8) )); // G. C. Greubel, Aug 24 2019
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^7)/(1-3*t+5*t^7-3*t^8)).list()
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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