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A162879
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Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
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1
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1, 42, 1722, 69741, 2824080, 114340800, 4629407580, 187434189600, 7588784431200, 307252630616400, 12439960566432000, 503665724648352000, 20392280251485912000, 825637071380896320000, 33428168171083640640000
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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 A170761, 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)/(820*t^3 - 40*t^2 - 40*t + 1).
a(n) = 40*a(n-1) + 40*a(n-2) - 820*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018
G.f.: (1+x)*(1-x^3)/(1 - 41*x + 860*x^3 - 820*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)/(820*x^3-40*x^2-40*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)/(820*t^3-40*t^2-40*t+1), {t, 0, 20}], t] (* Wesley Ivan Hurt, Apr 12 2017 *)
Join[{1}, LinearRecurrence[{40, 40, -820}, {42, 1722, 69741}, 20]] (* Vincenzo Librandi, Apr 14 2017 *)
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PROG
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(Magma) I:=[1, 42, 1722, 69741]; [n le 4 select I[n] else 40*Self(n-1) +40*Self(n-2)-820*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Apr 14 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 +2*t^2+2*t+1)/(820*t^3-40*t^2-40*t+1))); // G. C. Greubel, Oct 24 2018
(PARI) my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(820*t^3-40*t^2-40*t+1)) \\ G. C. Greubel, Oct 24 2018
(GAP) a:=[42, 1722, 69741];; for n in [4..20] do a[n]:=40*a[n-1]+40*a[n-2] -820*a[n-3]; od; Concatenation([1], a); # Muniru A Asiru, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1 -41*x +860*x^3 -820*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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