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A165756
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Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.
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1
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1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78726, 236160, 708432, 2125152, 6375024, 19123776, 57367440, 172090656, 516236976, 1548605952, 4645502958, 13935564252, 41803859076, 125403076764, 376183730628, 1128474698076
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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 A003946, 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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Index entries for linear recurrences with constant coefficients, signature (2,2,2,2,2,2,2,2,2,-3).
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FORMULA
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G.f.: (t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(3*t^10 - 2*t^9 - 2*t^8 - 2*t^7 - 2*t^6 - 2*t^5 - 2*t^4 - 2*t^3 - 2*t^2 - 2*t + 1).
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MAPLE
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seq(coeff(series((1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 16 2019
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MATHEMATICA
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CoefficientList[Series[(1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 07 2016 *)
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PROG
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(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11)) \\ G. C. Greubel, Sep 16 2019
(Magma) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11) )); // G. C. Greubel, Sep 16 2019
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11)).list()
(GAP) a:=[4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78726];; for n in [11..30] do a[n]:=2*Sum([1..9], j-> a[n-j]) -3*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 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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