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A165979
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Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
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2
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1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332001, 3811511582622900, 99099301147958475, 2576581829840760300, 66991127575699606500, 1741769316964025575200
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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 A170746, 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 (25, 25, 25, 25, 25, 25, 25, 25, 25, -325).
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FORMULA
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G.f.: (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)/(325*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).
G.f.: (1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11). - G. C. Greubel, Apr 26 2019
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11), {x, 0, 20}], x] (* G. C. Greubel, Apr 20 2016, modified Apr 26 2019 *)
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PROG
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(PARI) my(x='x+O('x^20)); Vec((1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11)) \\ G. C. Greubel, Apr 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11) )); // G. C. Greubel, Apr 26 2019
(Sage) ((1+x)*(1-x^10)/(1 -26*x +350*x^10 -325*x^11)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 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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