A316270 Number of tricolorable prime knots with n minimal crossings.

0, 0, 0, 1, 0, 0, 1, 2, 8, 21, 62, 210, 779, 3799

Offset

0,8

Links

Table of n, a(n) for n=0..13.

Y. Kiriu and K. Ouchi, Various Functions of Mathematica about the Knot Theory, 2007. [dead link]

C. Livingston and A. H. Moore, KnotInfo: Table of Knot Invariants.

Example

For n = 7, a(7)=2 because only 2 prime knots with minimal crossing number 7 are tricolorable: 7_4 and 7_7.

Crossrefs

Cf. A002863 (Number of prime knots with n crossings).

Sequence in context: A143229 A123285 A143212 * A219970 A107361 A185309

Adjacent sequences: A316267 A316268 A316269 * A316271 A316272 A316273

Keyword

nonn,hard,more

Author

Isaac Weiss, Henry Potts-Rubin, Jun 28 2018

Extensions

a(11)-a(13) using KnotInfo (taking the knots with determinant a multiple of 3) added by Andrey Zabolotskiy, Apr 29 2024

Status

approved