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 A357359 #9 Oct 01 2022 10:25:29 %S A357359 5,8,14,21,28,39,50 %N A357359 Maximum number of nodes in an induced path (or chordless path or snake path) in the n X n torus grid graph. %C A357359 It is somewhat unclear how a(n) should be defined for n <= 2. If the 1 X 1 and 2 X 2 torus grid graphs are considered to have loops and multiple edges, respectively, we have a(1) = 0 and a(2) = 1 (unless loops and multiple edges are allowed in a path), otherwise a(1) = 1 and a(2) = 3. %H A357359 Wikipedia, <a href="https://en.wikipedia.org/wiki/Induced_path">Induced path</a>. %F A357359 a(n) ~ 2*n^2/3. %F A357359 a(n) <= (2*n^2-1)/3. %F A357359 a(n) >= A357358(n) - 1. %F A357359 a(n) >= A331968(n-1). %e A357359 Longest induced paths (with one end in the lower left corner) for 3 <= n <= 7: %e A357359 . X X . X X . . X X . X . X X . X . . . . X . X X %e A357359 X X . X X . . . X . X X X X . X X . X X . X X . X %e A357359 X . . X . X . X X . X . X . X X . X . X X . X X . %e A357359 X . X . X . X X . . X X . X X X . X X . X X %e A357359 X . X . . X X . . X . X X . X . . . %e A357359 X . X . X . . X . X . X X %e A357359 X X . X . X . %Y A357359 Cf. A331968, A357234, A357358. %K A357359 nonn,more %O A357359 3,1 %A A357359 _Pontus von Brömssen_, Sep 25 2022