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%I #13 Aug 17 2020 22:13:29
%S 1,3,8,19,43,94,202,429,905,1901,3983,8332,17413,36370,75938,158519,
%T 330862,690523,1441082,3007369,6275917,13096737,27330418,57033206,
%U 119016808,248363751,518283950,1081551220,2256972626,4709831964,9828437634,20509899437,42799880699
%N Number of different positive braids with n crossings of 4 strands.
%D P. Xu, Growth of the positive braids semigroups, Journal of Pure and Applied Algebra, 1992.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-2,0,0,1).
%F G.f.: 1/(1-3*x+x^2+2*x^3-x^6).
%e a(3) = 19 = #{111, 112, 113, 121, 122, 123, 132, 133, 211, 213, 221, 222, 223, 232, 233, 321, 322, 332, 333}.
%t CoefficientList[Series[1/(1-3x+x^2+2x^3-x^6),{x,0,40}],x] (* _Harvey P. Dale_, Aug 01 2020 *)
%Y Cf. A000071, A054761.
%K nonn,easy
%O 0,2
%A Serge Burckel (burckel(AT)univ-reunion.fr), Apr 26 2000
%E More terms from _Benoit Cloitre_, Mar 22 2002