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A166691
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Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
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2
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1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518976, 4462207721088, 169563893401344, 6443427949251072, 244850262071540736, 9304309958718547227, 353563778431304766468, 13435423580389580056521
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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 A170758, 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 (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).
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FORMULA
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G.f.: (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)/(703*t^12 - 37*t^11 - 37*t^10 - 37*t^9 -37*t^8 -37*t^7 -37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).
G.f.: (1+x)*(1-x^12)/(1 -38*x +740*x^12 -703*x^13). - G. C. Greubel, Apr 26 2019
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1-x^12)/(1-38*x+740*x^12-703*x^13), {x, 0, 20}], x] (* G. C. Greubel, May 23 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^12)/(1-38*x+740*x^12-703*x^13)) \\ G. C. Greubel, Apr 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^12)/(1-38*x+740*x^12-703*x^13) )); // G. C. Greubel, Apr 26 2019
(Sage) ((1+x)*(1-x^12)/(1-38*x+740*x^12-703*x^13)).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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