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 A357357 #39 Feb 16 2025 08:34:04 %S A357357 0,4,8,12,16,20,32,40,50,62,76,90,104,120,140,160,180 %N A357357 Length of the longest induced cycle in the n X n grid graph. %H A357357 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 A357357 Elijah Beregovsky, <a href="/A357357/a357357.png">Illustration of initial terms</a>. %H A357357 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>. %H A357357 Wikipedia, <a href="https://en.wikipedia.org/wiki/Induced_path">Induced path</a>. %F A357357 a(n) <= A331968(n)+1. %F A357357 a(n) = 2*n^2/3 + O(n) (Beluhov 2023). - _Pontus von Brömssen_, Jan 30 2023 %e A357357 For 2 <= n <= 6, a longest induced cycle is the one going around the border of the grid, so a(n) = 4*(n-1). %e A357357 Longest induced cycles for 6 <= n <= 8: %e A357357 X X X X X X X X X X X X X X X X X X X X X %e A357357 X . . . . X X . . . . . X X . . . . . . X %e A357357 X . . . . X X . X X X . X X . X X X . X X %e A357357 X . . . . X X . X . X . X X . X . X . X . %e A357357 X . . . . X X . X . X . X X . X . X . X X %e A357357 X X X X X X X . X . X . X X . X . X . . X %e A357357 X X X . X X X X . X . X . . X %e A357357 X X X . X X X X %Y A357357 Main diagonal of A360915. %Y A357357 Cf. A000937, A297664, A331968, A357358, A360914 (number of longest induced cycles). %K A357357 nonn,more %O A357357 1,2 %A A357357 _Pontus von Brömssen_, Sep 25 2022 %E A357357 a(9)-a(12) from _Elijah Beregovsky_, Nov 24 2022 %E A357357 a(13) from _Elijah Beregovsky_, Nov 25 2022 %E A357357 a(14)-a(17) from _Andrew Howroyd_, Feb 26 2023