

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.


10



1, 2, 8, 42, 260, 1796, 13396, 105706, 870772, 7420836, 65004584, 582521748, 5320936416, 49402687392, 465189744448, 4434492302426, 42731740126228, 415736458808868, 4079436831493480, 40338413922226212, 401652846850965808, 4024556509468827432, 40558226664529024000, 410887438338905738908, 4182776248940752113344, 42770152711524569532616, 439143340987014152920384, 4526179842103708969039296
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OFFSET

0,2


COMMENTS

Also the number of knot diagrams with n crossings and two outgoing strings.


REFERENCES

V. I. Arnold, Topological Invariants of Plane Curves and Caustics, American Math. Soc., 1994.
S. M. GuseinZade, Adv. Sov. Math., v. 21 (1994), p. 189198.


LINKS

Table of n, a(n) for n=0..27.
S. R. Finch, Knots, links and tangles, August 8, 2003. [Cached copy, with permission of the author]
S. M. GuseinZade and F. S. Duzhin, On the number of topological types of plane curves; (Russian) Uspekhi Mat. Nauk 53 (1998), no. 3(321), 197198. English translation: Russian Mathematical Surveys 53 (1998) 626627. Related program and data.
J. L. Jacobsen and P. ZinnJustin, A Transfer Matrix approach to the Enumeration of Knots
J. L. Jacobsen and P. ZinnJustin, A Transfer Matrix approach to the Enumeration of Colored Links, J. Knot Theory, 10 (2001), 12331267.
P. ZinnJustin and J.B. Zuber. Knot theory and matrix integrals. In The Oxford Handbook of Random Matrix Theory. 2011. Eds Akemann, Baik and Di Francesco. arXiv.
Index entries for sequences related to knots


CROSSREFS

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


KEYWORD

nonn,nice


AUTHOR

Sergei Duzhin, Nov 11 2000


EXTENSIONS

Extended to n = 22 by J. L. Jacobsen and Paul ZinnJustin, Jan 30 2002
More terms from Paul ZinnJustin, Dec 13 2016


STATUS

approved



