Search: id:A054993
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%I A054993
%S A054993 1,2,8,42,260,1796,13396,105706,870772,7420836,65004584,582521748,
%T A054993 5320936416,49402687392,465189744448,4434492302426,42731740126228,
%U A054993 415736458808868,4079436831493480,40338413922226212,401652846850965808,
               4024556509468827432,40558226664529024000
%N A054993 Number of "long curves", i.e. topological types of smooth embeddings 
               of the oriented real line into the oriented plane that coincide with 
               the standard immersion x -> (x,0) in the neighborhood of -infty and 
               +infty.
%C A054993 Also the number of knot diagrams with n crossings and two outgoing strings.
%D A054993 V. I. Arnold, Topological Invariants of Plane Curves..., American Math. 
               Soc., 1994, p. A054993 S. M. Gusein-Zade, Adv. Sov. Math., v. 21 
               (1994), p. 189-198.
%H A054993 S. M. Gusein-Zade and F. S. Duzhin, <a href="http://www.botik.ru/~duzhin/
               as/dataprog/">On the number of topological types of plane curves</
               a>; (Russian) Uspekhi Mat. Nauk 53 (1998), no. 3(321), 197-198. English 
               translation: Russian Mathematical Surveys 53 (1998) 626-627.
%H A054993 J. L. Jacobsen and P. Zinn-Justin, <a href="http://arXiv.org/abs/math-ph/
               0102015">A Transfer Matrix approach to the Enumeration of Knots</
               a>
%H A054993 J. L. Jacobsen and P. Zinn-Justin, <a href="http://arXiv.org/abs/math-ph/
               0104009">A Transfer Matrix approach to the Enumeration of Colored 
               Links</a>, J. Knot Theory, 10 (2001), 1233-1267.
%H A054993 S. R. Finch, <a href="http://algo.inria.fr/bsolve/">Knots, links and 
               tangles</a>
%Y A054993 Cf. A008980, A008981, A008982, A008983, A008984, A008985.
%Y A054993 Cf. A067647, A067648.
%Y A054993 A column of the triangles in A067640 and A062038.
%Y A054993 Sequence in context: A107588 A013999 A130649 this_sequence A005315 A121635 
               A002874
%Y A054993 Adjacent sequences: A054990 A054991 A054992 this_sequence A054994 A054995 
               A054996
%K A054993 nonn,nice
%O A054993 0,2
%A A054993 Sergei V. Duzhin (duzhin(AT)botik.ru), Nov 11, 2000.
%E A054993 Extended to n = 22 by J. L. Jacobsen and P. Zinn-Justin, Jan 30, 2002

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