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A163218
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Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.
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1
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1, 35, 1190, 40460, 1375045, 46731300, 1588176975, 53974651500, 1834344072330, 62340711467265, 2118667029023160, 72003509011079415, 2447059985777227590, 83164038200838759780, 2826353783752411211145, 96054447135432681999180
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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 A170754, 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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FORMULA
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G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).
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MATHEMATICA
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CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(561*t^4-33*t^3-33*t^2 - 33*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{33, 33, 33, -561}, {1, 35, 1190, 40460}, 20] (* G. C. Greubel, Dec 11 2016 *)
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PROG
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(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(561*t^4-33*t^3 - 33*t^2-33*t+1)) \\ G. C. Greubel, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-34*x+594*x^4-x^561*x^5) )); // G. C. Greubel, Apr 30 2019
(Sage) ((1+x)*(1-x^4)/(1-34*x+594*x^4-561*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 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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