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A374947 a(n) is the number of suitably connected Legendrian n-Mosaics. 7
1, 2, 20, 1504, 948032, 5204262912 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
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. Note that the n-mosaic consisting of all blank tiles are considered as suitably connected although it is not representing a link.
LINKS
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 are exactly a(2) = 2 suitably connected Legendrian 2-mosaics, namely the empty mosaic and the Legendrian unknot with maximal Thurston-Bennequin invariant.
PROG
(Rust) // See Margaret Kipe link
CROSSREFS
Sequence in context: A112359 A308231 A179594 * A196749 A263417 A053848
KEYWORD
nonn,hard,more,new
AUTHOR
STATUS
approved

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Last modified August 18 14:27 EDT 2024. Contains 375269 sequences. (Running on oeis4.)