A374946 a(n) is the number of suitably connected Legendrian n-mosaics that form a Legendrian knot.

0, 1, 17, 793, 275557, 831699598

Offset: 1

Author

Margaret Kipe, Samantha Pezzimenti, Leif Schaumann, Luc Ta, Wing Hong Tony Wong, Jul 24 2024

Keywords

• nonn
• hard
• more

Comments

A Legendrian n-mosaic is an n X n array of the 10 tiles given in Figure 5 of Pezzimenti and Pandey. These tiles represent part of a Legendrian curve in the front projection. A Legendrian n-mosaic is suitably connected if the connection points of each tile coincide with those of the contiguous tiles.

Examples

			For n = 2 there is exactly a(2) = 1 Legendrian 2-mosaic forming the front projection of a Legendrian knot, namely the Legendrian unknot with maximal Thurston-Bennequin invariant.
		

Links

• Margaret Kipe, Python
• Margaret Kipe, Rust
• S. Pezzimenti and A. Pandey, Geography of Legendrian knot mosaics, Journal of Knot Theory and its Ramifications, 31 (2022), article no. 2250002, 1-22.

Crossrefs

Cf. A374947, A374945, A374944, A374943, A374942, A374939.