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A162881
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Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
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1
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1, 43, 1806, 74949, 3109932, 129025155, 5353007478, 222085686501, 9213895794684, 382266301290027, 15859472304395790, 657978118553895573, 27298209939779232636, 1132548704737573481379, 46987204341696557186262
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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 A170762, 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^3 + 2*t^2 + 2*t + 1)/(861*t^3 - 41*t^2 - 41*t + 1).
a(n) = 41*a(n-1) + 41*a(n-2) - 861*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018
G.f.: (1+x)*(1-x^3)/(1 -42*x + 902*x^3 - 861*x^4). - G. C. Greubel, Apr 27 2019
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MAPLE
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seq(coeff(series((x^3+2*x^2+2*x+1)/(861*x^3-41*x^2-41*x+1), x, n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 24 2018
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MATHEMATICA
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CoefficientList[Series[(t^3+2*t^2+2*t+1)/(861*t^3-41*t^2-41*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)
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PROG
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(PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(861*t^3-41*t^2-41*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(861*t^3-41*t^2-41*t+1))); // G. C. Greubel, Oct 24 2018
(GAP) a:=[43, 1806, 74949];; for n in [4..20] do a[n]:=41*a[n-1]+41*a[n-2] -861*a[n-3]; od; Concatenation([1], a); # Muniru A Asiru, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1 -42*x +902*x^3 -861*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 27 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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