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A166379
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Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.
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2
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1, 14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991222, 1930018885795, 25090245514152, 326173191668688, 4240251491494200, 55123269386840928, 716602501995344328
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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 A170733, 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 (12, 12, 12, 12, 12, 12, 12, 12, 12, 12, -78).
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FORMULA
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G.f.: (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)/(78*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).
G.f.: (1+x)*(1-x^11)/(1 -13*x +90*x^11 -78*x^12). - G. C. Greubel, Apr 26 2019
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1-x^11)/(1 -13*x +90*x^11 -78*x^12), {x, 0, 20}], x] (* G. C. Greubel, May 10 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^11)/(1-13*x+90*x^11-78*x^12)) \\ G. C. Greubel, Apr 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^11)/(1-13*x+90*x^11-78*x^12) )); // G. C. Greubel, Apr 26 2019
(Sage) ((1+x)*(1-x^11)/(1-13*x+90*x^11-78*x^12)).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,easy
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AUTHOR
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STATUS
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approved
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