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A164352
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Number of reduced words of length n in Coxeter group on 3 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.
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1
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1, 3, 6, 12, 24, 48, 96, 189, 372, 735, 1452, 2868, 5664, 11184, 22086, 43617, 86136, 170103, 335922, 663384, 1310064, 2587140, 5109132, 10089609, 19925148, 39348555, 77706264, 153455784, 303047352, 598463580, 1181857074, 2333953461
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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 A003945, 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^6 + t^5 + t^4 + t^3 + t^2 + t + 1)/(t^6 - 2*t^5 + t^4 - 2*t^3 + t^2 - 2*t + 1).
a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-a(n-4)+2*a(n-5)-a(n-6). - Wesley Ivan Hurt, May 11 2021
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MAPLE
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seq(coeff(series((1-t^7)/((1-t)*(1-2*t+t^2-2*t^3+t^4-2*t^5+t^6)), t, n+1), t, n), n = 0 .. 35); # G. C. Greubel, Aug 24 2019
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MATHEMATICA
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CoefficientList[Series[(1-t^7)/((1-t)*(1-2*t+t^2-2*t^3+t^4-2*t^5+t^6)), {t, 0, 35}], t] (* G. C. Greubel, Sep 15 2017 *)
LinearRecurrence[{2, -1, 2, -1, 2, -1}, {1, 3, 6, 12, 24, 48, 96}, 40] (* Harvey P. Dale, May 21 2021 *)
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PROG
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(PARI) (t='t+O('t^35)); Vec((1-t^7)/((1-t)*(1-2*t+t^2-2*t^3+t^4-2*t^5 +t^6))) \\ G. C. Greubel, Sep 15 2017
(Magma) R<t>:=PowerSeriesRing(Integers(), 35); Coefficients(R!( (1-t^7)/( (1-t)*(1-2*t+t^2-2*t^3+t^4-2*t^5+t^6)) )); // G. C. Greubel, Aug 24 2019
(Sage)
P.<t> = PowerSeriesRing(ZZ, prec)
return P((1-t^7)/((1-t)*(1-2*t+t^2-2*t^3+t^4-2*t^5+t^6))).list()
(GAP) a:=[3, 6, 12, 24, 48, 96];; for n in [7..35] do a[n]:=2*a[n-1] -a[n-2]+2*a[n-3]-a[n-4]+2*a[n-5]-a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 24 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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