A048952
Prime 2-component links with n crossings.
Original entry on oeis.org
0, 1, 0, 1, 1, 3, 8, 16, 61, 185, 638, 2818, 11292
Offset: 1
- D. Rolfsen, Knots and Links. Wilmington, DE: Publish or Perish Press, 1976.
- D. J. A. Welsh, On the number of knots and links, Sets, Graphs and Numbers (Budapest, 1991) 713-718, Colloq. Math. Soc. Janos Bolyai, 60, North-Holland, Amsterdam, 1992.
- D. Bar-Natan, The Thistlethwaite Link Table.
- Dylan Joshua Faullin, The Classification of Links of Up To And Including Thirteen Crossings, Master's Thesis, University of Tennessee, 2005.
- S. R. Finch, Knots, links and tangles [dead link]
- S. R. Finch, Knots, links and tangles, Aug 08 2003. [Cached copy, with permission of the author]
- Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 627.
- R. G. Scharein, Number of Prime Links.
- Eric Weisstein's World of Mathematics, Prime Link
A049344
Prime unoriented alternating links (not necessarily connected knots) with n crossings.
Original entry on oeis.org
0, 1, 1, 2, 3, 8, 14, 39, 96, 297, 915, 3308, 12417, 51347, 222595, 1016975, 4799520, 23301779, 115405815, 581071711, 2963793396, 15283327150, 79544488072, 417377448058
Offset: 1
- S. R. Finch, Knots, links and tangles [dead link]
- S. R. Finch, Knots, links and tangles, Aug 08 2003. [Cached copy, with permission of the author]
- Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 626.
- Bruce Fontaine, Knots/Links
- Stavros Garoufalidis and Thao Vuong, Alternating knots, planar graphs, and q-series, The Ramanujan Journal 36.3 (2015): 501-527; arXiv:1304.1071 [math.GT], 2013. See (28).
a(20)-a(24) from Bruce Fontaine's table (produced by him together with Stuart Rankin and Ortho Flint in 2007) added by
Andrey Zabolotskiy, Jun 08 2022
A086826
Number of nonsplittable links (prime or composite) with n crossings.
Original entry on oeis.org
1, 0, 1, 1, 3, 4, 15, 24, 82
Offset: 0
a(5)=4 since we have 2 prime knots, as well as the Whitehead link; and the trefoil knot linked with a circle.
a(6)=15 since we have 3 prime knots, as well as 2 composite knots (the square & granny knots); 6 prime links; a chain of four circles simply-intertwined; four circles simply-intertwined in the shape of a "T"; three circles, two doubly-intertwined and two simply-intertwined; and the figure-eight knot linked with a circle.
A087071
Number of distinct prime 4-component links with crossing number n.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 3, 1, 25, 39, 307, 1161
Offset: 1
Showing 1-4 of 4 results.
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