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A167961
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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)^16 = I.
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1
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1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501434880, 632170063134720, 27815482777927680, 1223881242228817920, 53850774658067988480, 2369434084954991493120, 104255099738019625697280
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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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Index entries for linear recurrences with constant coefficients, signature (43,43,43,43,43,43,43,43,43,43, 43,43,43,43,43,-946).
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FORMULA
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G.f.: (t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*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)/( 946*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
G.f.: (1 + x)*(1 + x^16)/(1 - 44*x + 946*x^16 - 903*x^17).
a(n) = 43*Sum_{k=1..15} a(n-k) - 946*a(n-16). (End)
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1+x^16)/(1-44*x+946*x^16-903*x^17), {x, 0, 50}], x] (* G. C. Greubel, Jul 02 2016; Apr 27 2023 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1+x^16)/(1-44*x+946*x^16-903*x^17) )); // G. C. Greubel, Apr 27 2023
(SageMath)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x)*(1+x^16)/(1-44*x+946*x^16-903*x^17) ).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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