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A163222
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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)^4 = I.
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1
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1, 39, 1482, 56316, 2139267, 81263988, 3086962281, 117263934684, 4454486050560, 169211838474861, 6427822638540342, 244172655087350379, 9275347010187982854, 352341101130365494992, 13384324210123816783899
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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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FORMULA
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G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).
a(n) = 37*a(n-1)+37*a(n-2)+37*a(n-3)-703*a(n-4). - Wesley Ivan Hurt, May 06 2021
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MATHEMATICA
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CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(703*t^4-37*t^3-37*t^2 - 37*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[{37, 37, 37, -703}, {39, 1482, 56316, 2139267}, 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)/(703*t^4-37*t^3 - 37*t^2-37*t+1)) \\ _G. c. Greubel_, Dec 11 2016
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-38*x+740*x^4-703*x^5) )); // G. C. Greubel, Apr 30 2019
(Sage) ((1+x)*(1-x^4)/(1-38*x+740*x^4-703*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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