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A168848
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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)^20 = I.
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0
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1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352
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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.
First disagreement at index 20: a(20) = 20694616160409771042814820001, A170746(20) = 20694616160409771042814820352. - Klaus Brockhaus, Apr 02 2011
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, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).
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FORMULA
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G.f.: (t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*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)/(325*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*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).
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MATHEMATICA
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CROSSREFS
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Cf. A170746 (G.f.: (1+x)/(1-26*x)).
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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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