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 A357500 #23 Jan 31 2023 01:13:15 %S A357500 1,1,7,9,15,21,24,34 %N A357500 Largest number of nodes of an induced path in the n X n knight graph. %D A357500 Thomas Dawson, Échecs Féeriques, L'Échiquier, volume 2, issue 2, 1930; issue 3, 1931. %D A357500 Donald E. Knuth, The Art of Computer Programming, Volume 4B, Combinatorial Algorithms, Part 2, Addison-Wesley, 2023. See exercise 7.2.2.1-172 and its solution. %H A357500 Nikolai Beluhov, <a href="https://arxiv.org/abs/2301.01152">Snake paths in king and knight graphs</a>, arXiv:2301.01152 [math.CO], 2023. %H A357500 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KnightGraph.html">Knight Graph</a>. %H A357500 Wikipedia, <a href="https://en.wikipedia.org/wiki/Induced_path">Induced path</a> %F A357500 a(n) >= A165143(n) - 1 for n >= 3. %F A357500 a(n) <= (4*(n^2+3*n-2)-1)/7 for n >= 4. - _Elijah Beregovsky_, Dec 22 2022 %F A357500 a(n) = n^2/2 + O(n) (Beluhov 2023). - _Pontus von Brömssen_, Jan 30 2023 %e A357500 Longest paths for 3 <= n <= 7: %e A357500 X . X . . . . . X . X . . X X X . . X . X X X . . %e A357500 X . X X . X X X X . X X X . . X X X X . X . . X . %e A357500 X X X . X X . X . . . X X . . . X X . X X . . X . %e A357500 X X X X X X . X X X X . . . X . . X . . X X %e A357500 . X X X . . X X . X X . . . . . . X %e A357500 . X X X X . . X X X X X X %e A357500 X X . X X . . %Y A357500 Cf. A165143, A331968. %K A357500 nonn,more %O A357500 1,3 %A A357500 _Pontus von Brömssen_, Oct 01 2022