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Search: id:A059739
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| A059739 |
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Triangle T(n,k), n >= 1, giving number of prime unoriented alternating links with n crossings and k components. |
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+0
4
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| 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
(list; graph; listen)
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OFFSET
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0,7
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COMMENT
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A link is a not necessarily connected knot. Apart from the initial rows, the n-th row contains [n/2] terms.
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REFERENCES
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Ortho Flint, Bruce Fontaine and Stuart Rankin, Enumerating the prime alternating links, preprint, 2007.
Ortho Flint, Bruce Fontaine and Stuart Rankin, The master array of a prime alternating link, preprint, 2007
Ortho Flint and Stuart Rankin, Enumerating the prime alternating links, Journal of Knot theory and its Ramifications, 13 (2004), 151-173.
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LINKS
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Stuart Rankin (srankin(AT)uwo.ca), Nov 05 2007, Table of n, a(n) for n = 0..133
M. B. Thistlethwaite, Home Page
M. B. Thistlethwaite, Numbers of knots and links with up to 19 crossings
S. R. Finch, Knots, links and tangles
Knotilus web site, Knotilus.
Rankin and Flint knot theory web page.
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EXAMPLE
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0; 0,1; 1; 1,1; 2,1; 3,3,2; 7,6,1; 18,14,6,1; 41,42,12,1; ...
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CROSSREFS
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First column gives numbers of knots, A002864. Second column gives A059741. Row sums give A049344.
Sequence in context: A144305 A138635 A128182 this_sequence A035566 A110783 A124770
Adjacent sequences: A059736 A059737 A059738 this_sequence A059740 A059741 A059742
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KEYWORD
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nonn,tabf,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Feb 10 2001
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EXTENSIONS
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The terms for the 20, 21, 22 and 23 crossing prime alternating links (see the b-file) were added Nov 03, 2007 by Stuart Rankin, Ortho Flint and Bruce Fontaine.
The trailing 0 in the row for n=2 was removed by N. J. A. Sloane (njas(AT)research.att.com), Nov 21 2007
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