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 A374939 #17 Aug 09 2024 08:01:26 %S A374939 0,1,4,9,40,328 %N A374939 a(n) is the number of distinct Legendrian knots, up to smooth knot type and classical invariants, with nonnegative rotation numbers that can be realized on a Legendrian n-mosaic. %C A374939 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 A374939 The classical invariants of Legendrian knots are the Thurston-Bennequin invariant and the rotation number. %H A374939 Margaret Kipe, <a href="/A374939/a374939.py.txt">Python</a> %H A374939 Margaret Kipe, <a href="/A374939/a374939.rs.txt">Rust</a> %H A374939 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 A374939 For n = 3 there are exactly a(3) = 4 distinct Legendrian knots with nonnegative rotation numbers that can be realized on a Legendrian 3-mosaic, namely the four Legendrian unknots whose Thurston-Bennequin invariants are -1, -2, -3, and -3 and whose rotation numbers are 0, 1, 0, and 2, respectively. %o A374939 (Python, Rust) //See Margaret Kipe links %Y A374939 Cf. A374942, A374943, A374944, A374945, A374946, A374947. %K A374939 nonn,hard,more %O A374939 1,3 %A A374939 _Margaret Kipe_, _Samantha Pezzimenti_, _Leif Schaumann_, _Luc Ta_, _Wing Hong Tony Wong_, Jul 24 2024