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A162851
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Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.
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1
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1, 37, 1332, 47286, 1678320, 59557050, 2113447770, 74997827100, 2661373678950, 94441530616650, 3351353019273000, 118926143828399250, 4220214225380039250, 149758560520153357500, 5314333645481777358750, 188584492248078150341250
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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 A170756, 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)/(630*t^3 - 35*t^2 - 35*t + 1).
G.f.: (1+x)*(1-x^3)/(1 - 36*x + 665*x^3 - 630*x^4). - G. C. Greubel, Apr 26 2019
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MATHEMATICA
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CoefficientList[Series[(t^3+2*t^2+2*t+1)/(630*t^3-35*t^2-35*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{35, 35, -630}, {1, 37, 1332}, 20] (* 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)/(630*t^3-35*t^2-35*t+1)) \\ G. C. Greubel, Oct 24 2018
(Magma) R<t>:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 +2*t^2+2*t+1)/(630*t^3-35*t^2-35*t+1))); // G. C. Greubel, Oct 24 2018
(Sage) ((1+x)*(1-x^3)/(1-36*x+665*x^3-630*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019
(GAP) a:=[37, 1332, 47286];; for n in [4..20] do a[n]:=35*a[n-1]+ 35*a[n-2]-630*a[n-3]; od; Concatenation([1], a); # G. C. Greubel, Apr 26 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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