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A163829
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Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
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3
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1, 48, 2256, 106032, 4983504, 234223560, 11008454304, 517394861664, 24317441438880, 1142914245838944, 53716710971646072, 2524673262335033136, 118659072125876564688, 5576949543463542381360, 262115366765585626863312
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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 A170767, 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.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
G.f.: (1+x)*(1-x^5)/(1 -47*x +1127*x^5 -1081*x^6). - G. C. Greubel, Apr 25 2019
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1-x^5)/(1-47*x+1127*x^5-1081*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 05 2017, modified Apr 25 2019 *)
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PROG
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(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-47*x+1127*x^5-1081*x^6)) \\ G. C. Greubel, Aug 05 2017, modified Apr 25 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-47*x+1127*x^5-1081*x^6) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^5)/(1-47*x+1127*x^5-1081*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
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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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