A094029 Number of n-crossing links with alternating braids of 3 strands.

1, 1, 4, 5, 13, 18, 38, 57, 115, 183, 354, 604, 1153, 2047, 3904, 7145, 13637, 25471, 48722, 92193

Offset: 4

Author

Thomas A. Gittings, Apr 22 2004

Keywords

• nonn
• more

Comments

Series is sum of three series for 1, 2 and 3 component links with alternating braids of 3 strands.

Examples

			4 crossing knot (1 component link) can be represented as 3-strand braid AbAb that is alternating (overcrossings and undercrossing alternate).
		

References

• K. Murasugi and B. J. Kurpita, A Study of Braids, Kluwer Academic Publishers (1999), pp. 127-166

Links

• T. A. Gittings, Minimum braids: a complete invariant of knots and links.
• V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math., 126 (1987), pp. 335-388.

Crossrefs

Cf. A094030, A094031, A094032.