A059739 Triangle T(n,k), n >= 1, giving number of prime unoriented alternating links with n crossings and k components.
0, 0, 1, 1, 1, 1, 2, 1, 3, 3, 2, 7, 6, 1, 18, 14, 6, 1, 41, 42, 12, 1, 123, 121, 43, 9, 1, 367, 384, 146, 17, 1, 1288, 1408, 500, 100, 11, 1, 4878, 5100, 2074, 341, 23, 1, 19536, 21854, 8206, 1556, 181, 13, 1, 85263, 92234, 37222, 7193, 653, 29, 1, 379799, 427079, 172678, 33216, 3885, 301, 16, 1, 1769979, 2005800, 829904, 173549, 19122, 1129, 36, 1, 8400285, 9716848, 4194015, 876173, 105539, 8428, 471, 19, 1, 40619385, 48184018, 21207695, 4749914, 599433, 43513, 1813, 43, 1
Offset: 0
Examples
First few rows of irregular triangle: 0 0 1 1 1 1 2 1 3 3 2 7 6 1 18 14 6 1 41 42 12 1 ...
References
- Ortho Flint, Bruce Fontaine and Stuart Rankin, The master array of a prime alternating link, preprint, 2007
Links
- Stuart Rankin (srankin(AT)uwo.ca), Nov 05 2007, Table of n, a(n) for n = 0..133
- Steven R. Finch, Knots, links and tangles, August 8, 2003. [Cached copy, with permission of the author]
- Ortho Flint, Bruce Fontaine and Stuart Rankin, Enumerating the prime alternating links, preprint, 2007.
- Ortho Flint and Stuart Rankin, Enumerating the prime alternating links, Journal of Knot theory and its Ramifications, 13 (2004), 151-173.
- Knotilus web site, Knotilus. [dead link]
- S. Rankin and O. Flint, Knot theory web page.
- M. B. Thistlethwaite, Home Page.
- M. B. Thistlethwaite, Numbers of knots and links with up to 19 crossings.
- Index entries for sequences related to knots
Crossrefs
Extensions
Terms for the 20-, 21-, 22- and 23-crossing prime alternating links (see the b-file) added Nov 03 2007 by Stuart Rankin, Ortho Flint and Bruce Fontaine
Trailing 0 in row for n=2 removed by N. J. A. Sloane, Nov 21 2007
Comments