A163566 Total number of grid diagrams of nontrivial knots on grid size n.

10, 972, 85022, 8077072

Offset

5,1

Comments

From page 3 of Baldridge/McCarthy reference.

Note that creating grid diagrams with sizes above 8 is time intensive and the computation to rule out unknot grid diagrams grows quickly beyond the capabilities of most computers. Baldridge and McCarty highlight some of the differences between cube diagrams and grid diagrams, list examples of small cube diagrams for all knots up to 7 crossings, and give some examples of links.

Links

Table of n, a(n) for n=5..8.

Scott Baldridge, Ben McCarty, Small examples of cube diagrams of knots, July 30, 2009.

Example

The table on p.3 may be shown, where b(n) = Number that lift to cube diagrams:
==========================================
.n.|..a(n)...|...b(n)..|.b(n) as % of a(n)
...|.........|.........|.................
.5.|......10.|.......3.|.30%.............
.6.|.....972.|.....261.|.27%.............
.7.|...85022.|...19722.|.23%.............
.8.|.8077072.|.1589447.|.19.7%...........
==========================================

Crossrefs

Sequence in context: A292669 A159869 A006242 * A168520 A200993 A365704

Adjacent sequences: A163563 A163564 A163565 * A163567 A163568 A163569

Keyword

nonn

Author

Jonathan Vos Post, Jul 30 2009

Status

approved