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A163564
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Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.
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1
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1, 31, 930, 27900, 837000, 25109535, 753272100, 22597744965, 677919807900, 20337218005500, 610105253435760, 18302819007466125, 549074412543683490, 16471927651538698875, 494148687972122850750, 14824186397015923722360
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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 A170750, 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)/(435*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).
a(n) = 29*a(n-1)+29*a(n-2)+29*a(n-3)+29*a(n-4)-435*a(n-5). - Wesley Ivan Hurt, May 11 2021
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MATHEMATICA
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With[{num=Total[2t^Range[4]]+t^5+1, den=Total[-29 t^Range[4]]+435t^5+1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Sep 16 2011 *)
CoefficientList[Series[(1+x)*(1-x^5)/(1-30*x+464*x^5-435*x^6), {x, 0, 20}], x] (* or *) coxG[{5, 435, -29}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 18 2019 *)
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PROG
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(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-30*x+464*x^5-435*x^6)) \\ G. C. Greubel, Jul 28 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-30*x+464*x^5-435*x^6) )); // G. C. Greubel, May 18 2019
(Sage) ((1+x)*(1-x^5)/(1-30*x+464*x^5-435*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 18 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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