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A162889
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Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
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1
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1, 46, 2070, 92115, 4098600, 182342160, 8112199590, 360902223000, 16056115855560, 714317717862540, 31779155482826400, 1413817266133308960, 62899068010426041240, 2798305588240613272800, 124493325781573753947360
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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 A170765, 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)/(990*t^3 - 44*t^2 - 44*t + 1).
a(n) = 44*a(n-1) + 44*a(n-2) - 990*a(n-3).
G.f.: (1+x)*(1-x^3)/(1 - 45*x + 1034*x^3 - 990*x^4). (End)
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MATHEMATICA
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CoefficientList[Series[(t^3+2*t^2+2*t+1)/(990*t^3-44*t^2-44*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)/(990*t^3-44*t^2-44*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(990*t^3-44*t^2-44*t+1))); // G. C. Greubel, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1-45*x+1034*x^3-990*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019
(GAP) a:=[46, 2070, 92115];; for n in [4..20] do a[n]:=44*a[n-1]+44*a[n-2] - 990*a[n-3]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 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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