%I A059739
%S A059739 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,
%T A059739 19536,21854,8206,1556,181,13,1,85263,92234,37222,7193,653,29,1,379799,
               427079,172678,33216,3885,301,16,1,
%U A059739 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
%N A059739 Triangle T(n,k), n >= 1, giving number of prime unoriented alternating 
               links with n crossings and k components.
%C A059739 A link is a not necessarily connected knot. Apart from the initial rows, 
               the n-th row contains [n/2] terms.
%D A059739 Ortho Flint, Bruce Fontaine and Stuart Rankin, Enumerating the prime 
               alternating links, preprint, 2007.
%D A059739 Ortho Flint, Bruce Fontaine and Stuart Rankin, The master array of a 
               prime alternating link, preprint, 2007
%D A059739 Ortho Flint and Stuart Rankin, Enumerating the prime alternating links, 
               Journal of Knot theory and its Ramifications, 13 (2004), 151-173.
%H A059739 Stuart Rankin (srankin(AT)uwo.ca), Nov 05 2007, <a href="b059739.txt">
               Table of n, a(n) for n = 0..133</a>
%H A059739 M. B. Thistlethwaite, <a href="http://www.math.utk.edu/~morwen/index.html">
               Home Page</a>
%H A059739 M. B. Thistlethwaite, <a href="http://www.math.utk.edu/~morwen/png/link_stats.png">
               Numbers of knots and links with up to 19 crossings</a>
%H A059739 S. R. Finch, <a href="http://algo.inria.fr/bsolve/">Knots, links and 
               tangles</a>
%H A059739 Knotilus web site, <a href="http://knotilus.math.uwo.ca">Knotilus</a>
               .
%H A059739 Rankin and Flint <a href="http://www.math.uwo.ca/~srankin/knots/knotprint.html">
               knot theory</a> web page.
%e A059739 0; 0,1; 1; 1,1; 2,1; 3,3,2; 7,6,1; 18,14,6,1; 41,42,12,1; ...
%Y A059739 First column gives numbers of knots, A002864. Second column gives A059741. 
               Row sums give A049344.
%Y A059739 Sequence in context: A144305 A138635 A128182 this_sequence A035566 A110783 
               A124770
%Y A059739 Adjacent sequences: A059736 A059737 A059738 this_sequence A059740 A059741 
               A059742
%K A059739 nonn,tabf,nice
%O A059739 0,7
%A A059739 N. J. A. Sloane (njas(AT)research.att.com), Feb 10 2001
%E A059739 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.
%E A059739 The trailing 0 in the row for n=2 was removed by N. J. A. Sloane (njas(AT)research.att.com), 
               Nov 21 2007