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A097550
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Number of positive words of length n in the monoid Br_3 of positive braids on 4 strands.
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11
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1, 3, 8, 19, 44, 102, 237, 551, 1281, 2978, 6923, 16094, 37414, 86977, 202197, 470051, 1092736, 2540303, 5905488, 13728594, 31915109, 74193627, 172479257, 400965626, 932131991, 2166943978, 5037533578, 11710844769, 27224411129, 63289077427
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: (1 + q^2)/(1-3q+2q^2-q^3).
a(n) = term (1,1) in the 1x3 matrix [1,1,2].[3,1,0; -2,0,1; 1,0,0]^n. - Alois P. Heinz, Jul 24 2008
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MAPLE
| a:= n-> (Matrix([[1, 1, 2]]). Matrix([[3, 1, 0], [ -2, 0, 1], [1, 0, 0]])^n)[1, 1]: seq (a(n), n=0..50); # Alois P. Heinz, Jul 24 2008
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MATHEMATICA
| <<DiscreteMath`; Do[Print[SeriesTerm[(1 + q^2)/(1-3q+2q^2-q^3), {q, 0, n}]], {n, 0, 50}] (Propper)
a=1; b=2; c=3; lst={}; Do[AppendTo[lst, a+=b]; b+=c; c+=a, {n, 5!}]; lst [From Vladimir Orlovsky, Jan 20 2009]
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CROSSREFS
| Cf. A097551-A097556.
Sequence in context: A121551 A189391 A077850 * A079490 A026789 A096576
Adjacent sequences: A097547 A097548 A097549 * A097551 A097552 A097553
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KEYWORD
| nonn
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AUTHOR
| D. N. Verma (dnverma(AT)math.tifr.res.in), Aug 16 2004
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EXTENSIONS
| More terms from Ryan Propper (rpropper(AT)stanford.edu), Sep 27 2005
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