A054480 Number of different positive braids with n crossings of 4 strands.

1, 3, 8, 19, 43, 94, 202, 429, 905, 1901, 3983, 8332, 17413, 36370, 75938, 158519, 330862, 690523, 1441082, 3007369, 6275917, 13096737, 27330418, 57033206, 119016808, 248363751, 518283950, 1081551220, 2256972626, 4709831964, 9828437634, 20509899437, 42799880699

Offset

0,2

References

P. Xu, Growth of the positive braids semigroups, Journal of Pure and Applied Algebra, 1992.

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-2,0,0,1).

Formula

G.f.: 1/(1-3*x+x^2+2*x^3-x^6).

Example

a(3) = 19 = #{111, 112, 113, 121, 122, 123, 132, 133, 211, 213, 221, 222, 223, 232, 233, 321, 322, 332, 333}.

Mathematica

CoefficientList[Series[1/(1-3x+x^2+2x^3-x^6), {x, 0, 40}], x] (* Harvey P. Dale, Aug 01 2020 *)

Crossrefs

Cf. A000071, A054761.

Sequence in context: A259401 A008466 A102712 * A371796 A191787 A347310

Adjacent sequences: A054477 A054478 A054479 * A054481 A054482 A054483

Keyword

nonn,easy

Author

Serge Burckel (burckel(AT)univ-reunion.fr), Apr 26 2000

Extensions

More terms from Benoit Cloitre, Mar 22 2002

Status

approved