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A094029 Number of n-crossing links with alternating braids of 3 strands. 3
1, 1, 4, 5, 13, 18, 38, 57, 115, 183, 354, 604, 1153, 2047, 3904, 7145, 13637, 25471, 48722, 92193 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,3

COMMENTS

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

REFERENCES

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

LINKS

Table of n, a(n) for n=4..23.

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.

EXAMPLE

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

CROSSREFS

Cf. A094030, A094031, A094032.

Sequence in context: A091183 A234254 A258281 * A005672 A147001 A247325

Adjacent sequences:  A094026 A094027 A094028 * A094030 A094031 A094032

KEYWORD

nonn,more

AUTHOR

Thomas A. Gittings, Apr 22 2004

STATUS

approved

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Last modified October 16 07:07 EDT 2021. Contains 348041 sequences. (Running on oeis4.)