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A168680
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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)^17 = I.
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1
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1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196605, 393204, 786399, 1572780, 3145524, 6290976, 12581808, 25163328, 50326080, 100651008, 201299712, 402594816, 805180416, 1610342400, 3220647936
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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,-1,2,-1,2,-1,2,-1).
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FORMULA
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G.f.: (t^16 + t^15 + t^14 + t^13 + t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)/(t^16 - 2*t^15 + t^14 - 2*t^13 + t^12 - 2*t^11 + 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).
G.f.: (1+t)*(1-t^17)/(1 -2*t +2*t^17 -t^18). - G. C. Greubel, Feb 22 2021
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MATHEMATICA
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CoefficientList[Series[(1+t)*(1-t^17)/(1 -2*t +2*t^17 -t^18), {t, 0, 40}], t] (* G. C. Greubel, Jul 29 2016, Feb 22 2021 *)
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PROG
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(PARI) Vec(Pol(vector(17, i, 1))/Pol(vector(17, i, if(i%2, 1, -2)))+O(x^99)) \\ Charles R Greathouse IV, Jul 30 2016
(Magma)
R<t>:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+t)*(1-t^17)/(1 -2*t +2*t^17 -t^18) )); // G. C. Greubel, Feb 22 2021
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P( (1+t)*(1-t^17)/(1 -2*t +2*t^17 -t^18) ).list()
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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