A086826 Number of nonsplittable links (prime or composite) with n crossings.

1, 0, 1, 1, 3, 4, 15, 24, 82

Offset: 0

Author

Steven Finch, Aug 07 2003

Keywords

• nonn

Comments

A link L is splittable if we can embed a plane in R^3, disjoint from L, that separates one or more components of L from other components of L. Otherwise L is nonsplittable.

Examples

			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.
		

Links

• S. R. Finch, Knots, links and tangles, August 8, 2003. [Cached copy, with permission of the author]
• Stéphane Legendre, Table of nonsplittable links
• Eric Weisstein's World of Mathematics, Splittable Link
• Index entries for sequences related to knots

Crossrefs

Cf. A086771, A086825.

Extensions

a(7) and a(8) from Stéphane Legendre, Jan 06 2014