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A002863 Number of prime knots with n crossings.
(Formerly M0851 N0323)
+0
11
0, 0, 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, 46972, 253293, 1388705 (list; graph; listen)
OFFSET

1,5

REFERENCES

C. C. Adams, The Knot Book, Freeman, NY, 2001; see p. 33.

J. H. Conway, An enumeration of knots and links and some of their algebraic properties. 1970. Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) pp. 329-358 Pergamon, Oxford.

Martin Gardner, The Last Recreations, Copernicus, 1997, 67-84.

J. Hoste, M. B. Thistlethwaite and J. Weeks, The First 1,701,936 Knots, Math. Intell., 20, 33-48, Fall 1998.

W. B. R. Lickorish and K. C. Millett, The new polynomial invariants of knots and links. Math. Mag. 61 (1988), no. 1, 3-23.

K. A. Perko, Jr., On the classification of knots, Proc. Amer. Math. Soc., 45 (1974), 262-266.

P. G. Tait, Scientific Papers, Cambridge Univ. Press, Vol. 1, 1898, Vol. 2, 1900, see Vol. 1, p. 345.

M. B. Thistlethwaite, personal communication.

M. B. Thistlethwaite, Knot tabulations and related topics. Aspects of topology, 1-76, London Math. Soc. Lecture Note Ser., 93, Cambridge Univ. Press, Cambridge-New York, 1985.

LINKS

S. R. Finch, Knots, links and tangles

R. G. Scharein, Number of Prime Links

N. J. A. Sloane, Illustration of initial terms

M. B. Thistlethwaite, Home Page

M. B. Thistlethwaite, Numbers of knots and links with up to 19 crossings

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (1).

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (2).

Eric Weisstein's World of Mathematics, Prime Link

CROSSREFS

Cf. A002864, A086825.

Adjacent sequences: A002860 A002861 A002862 this_sequence A002864 A002865 A002866

Sequence in context: A080021 A032313 A032223 this_sequence A047693 A001532 A109456

KEYWORD

nonn,hard,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

This is stated incorrectly in CRC Standard Mathematical Tables and Formulae, 30th ed., first printing, 1996, p. 320.

Terms from Hoste et al. added by Eric Weisstein (eric(AT)weisstein.com)

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Last modified July 3 11:28 EDT 2009. Contains 160562 sequences.


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