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 A374945 #17 Nov 11 2024 01:56:30 %S A374945 0,1,1,1,2,11 %N A374945 a(n) is the number of knots having a Legendrian representative realizable on a Legendrian n-mosaic. %C A374945 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 A374945 Two knots have the same smooth knot type if and only if they are related by an ambient isotopy. %H A374945 Margaret Kipe, <a href="/A374945/a374945.py.txt">Python</a> %H A374945 Margaret Kipe, <a href="/A374945/a374945.rs.txt">Rust</a> %H A374945 Margaret Kipe, Samantha Pezzimenti, Leif Schaumann, Luc Ta, and Wing Hong Tony Wong, <a href="http://arxiv.org/abs/2410.08064">Bounds on the mosaic number of Legendrian knots</a>, arXiv: 2410.08064 [math.GT], 2024. %H A374945 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 A374945 For n = 2, there is only a(2) = 1 smooth knot family with Legendrian representatives realizable on a Legendrian 2-mosaic, namely unknots. %e A374945 For n = 5, every Legendrian 5-mosaic depicts either an unknot or a trefoil. Since unknots and trefoils are not ambient-isotopic, we have a(5) = 2. %o A374945 (Python, Rust) //See Margaret Kipe links %Y A374945 Cf. A374939, A374942, A374943, A374944, A374946, A374947 %K A374945 hard,more,nonn %O A374945 1,5 %A A374945 _Margaret Kipe_, _Samantha Pezzimenti_, _Leif Schaumann_, _Luc Ta_, _Wing Hong Tony Wong_, Jul 24 2024