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A054993
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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.
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11
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1, 2, 8, 42, 260, 1796, 13396, 105706, 870772, 7420836, 65004584, 582521748, 5320936416, 49402687392, 465189744448, 4434492302426, 42731740126228, 415736458808868, 4079436831493480, 40338413922226212, 401652846850965808, 4024556509468827432, 40558226664529024000
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OFFSET
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0,2
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COMMENTS
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Also the number of knot diagrams with n crossings and two outgoing strings.
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=0..22.
S. R. Finch, Knots, links and tangles
S. M. Gusein-Zade and F. S. Duzhin, On the number of topological types of plane curves; (Russian) Uspekhi Mat. Nauk 53 (1998), no. 3(321), 197-198. English translation: Russian Mathematical Surveys 53 (1998) 626-627.
J. L. Jacobsen and P. Zinn-Justin, A Transfer Matrix approach to the Enumeration of Knots
J. L. Jacobsen and P. Zinn-Justin, A Transfer Matrix approach to the Enumeration of Colored Links, J. Knot Theory, 10 (2001), 1233-1267.
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CROSSREFS
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Cf. A008980, A008981, A008982, A008983, A008984, A008985.
Cf. A067647, A067648.
A column of the triangles in A067640 and A062038.
Sequence in context: A107588 A013999 A130649 * A188912 A229285 A005315
Adjacent sequences: A054990 A054991 A054992 * A054994 A054995 A054996
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KEYWORD
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nonn,nice
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AUTHOR
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Sergei Duzhin, Nov 11 2000
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EXTENSIONS
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Extended to n = 22 by J. L. Jacobsen and P. Zinn-Justin, Jan 30 2002
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STATUS
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approved
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