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A374946
a(n) is the number of suitably connected Legendrian n-mosaics that form a Legendrian knot.
12
0, 1, 17, 793, 275557, 831699598
OFFSET
1,3
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.
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.
EXAMPLE
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.
PROG
(Python, Rust) //See Margaret Kipe Links
CROSSREFS
KEYWORD
nonn,hard,more
STATUS
approved