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A166690
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Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.
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2
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1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248998, 4938546112212926, 182726206151878262, 6760869627619494991, 250152176221921288656, 9255630520211086718568
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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 A170757, 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 (36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, -666).
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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)/(666*t^12 - 36*t^11 - 36*t^10 - 36*t^9 -36*t^8 -36*t^7 -36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).
G.f.: (1+x)*(1-x^12)/(1 -37*x +702*x^6 -666*x^7). - G. C. Greubel, Apr 26 2019
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MATHEMATICA
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CoefficientList[Series[(1+x)*(1-x^12)/(1-37*x+702*x^6-666*x^7), {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)/(1-37*x+702*x^6-666*x^7)) \\ G. C. Greubel, Apr 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^12)/(1-37*x+702*x^6-666*x^7) )); // G. C. Greubel, Apr 26 2019
(Sage) ((1+x)*(1-x^12)/(1-37*x+702*x^6-666*x^7)).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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