This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A374943 #14 Aug 09 2024 08:02:27 %S A374943 0,1,4,9,21,55 %N A374943 a(n) is the number of distinct Legendrian unknots with nonnegative rotation numbers that can be realized on a Legendrian n-mosaic. %C A374943 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. %C A374943 By Theorem 1.5 of Eliashberg and Fraser, two Legendrian unknots are equivalent if and only if they share the same Thurston-Bennequin invariant and rotation number. %H A374943 Y. Eliashberg and M. Fraser, <a href="https://doi.org/10.48550/arXiv.0801.2553">Topologically trivial Legendrian knots</a>, Journal of Symplectic Geometry, 7 (2009), 77-127. %H A374943 Margaret Kipe, <a href="/A374943/a374943.py.txt">Python</a> %H A374943 Margaret Kipe, <a href="/A374943/a374943.rs.txt">Rust</a> %H A374943 S. Pezzimenti and A. Pandey, <a href="https://doi.org/10.1142/S021821652250002X">Geography of Legendrian knot mosaics</a>, Journal of Knot Theory and its Ramifications, 31 (2022), article no. 2250002, 1-22. %e A374943 For n = 3 there are exactly a(3) = 4 distinct Legendrian unknots that can be realized on a Legendrian 3-mosaic, namely those whose Thurston-Bennequin invariants are -1, -2, -3, and -3 and whose rotation numbers are 0, 1, 0, and 2, respectively. %o A374943 (Python, Rust) //See Margaret Kipe links %Y A374943 Cf. A374939, A374942, A374944, A374945, A374946, A374947. %K A374943 nonn,hard,more %O A374943 1,3 %A A374943 _Margaret Kipe_, _Samantha Pezzimenti_, _Leif Schaumann_, _Luc Ta_, _Wing Hong Tony Wong_, Jul 24 2024