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 A360917 #16 Feb 16 2025 08:34:04 %S A360917 1,2,2,3,3,3,4,5,5,4,5,6,7,6,5,6,8,9,9,8,6,7,9,11,11,11,9,7,8,11,14, %T A360917 14,14,14,11,8,9,12,16,17,17,17,16,12,9,10,14,18,20,21,21,20,18,14,10, %U A360917 11,15,20,22,24,24,24,22,20,15,11,12,17,22,25,27,29,29,27,25,22,17,12 %N A360917 Array read by antidiagonals: T(m,n) is the number of vertices in the longest induced path in the grid graph P_m X P_n. %C A360917 Equivalently, T(m,n) is the maximum number of unit squares of a snake-like polyomino in an m X n rectangle. %H A360917 Andrew Howroyd, <a href="/A360917/b360917.txt">Table of n, a(n) for n = 1..435</a> %H A360917 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 A360917 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>. %F A360917 T(m,n) = T(n,m). %F A360917 T(m,n) = 2*m*n/3 + O(m+n) (Beluhov 2023, Proposition 3). - _Pontus von Brömssen_, May 08 2023 %e A360917 Array begins: %e A360917 ============================================== %e A360917 m\n| 1 2 3 4 5 6 7 8 9 10 11 12 ... %e A360917 -----+---------------------------------------- %e A360917 1 | 1 2 3 4 5 6 7 8 9 10 11 12 ... %e A360917 2 | 2 3 5 6 8 9 11 12 14 15 17 18 ... %e A360917 3 | 3 5 7 9 11 14 16 18 20 22 24 26 ... %e A360917 4 | 4 6 9 11 14 17 20 22 25 28 30 33 ... %e A360917 5 | 5 8 11 14 17 21 24 27 30 34 37 40 ... %e A360917 6 | 6 9 14 17 21 24 29 32 36 40 44 47 ... %e A360917 7 | 7 11 16 20 24 29 33 38 42 46 50 55 ... %e A360917 8 | 8 12 18 22 27 32 38 42 48 52 57 62 ... %e A360917 9 | 9 14 20 25 30 36 42 48 53 58 64 70 ... %e A360917 10 | 10 15 22 28 34 40 46 52 58 64 71 77 ... %e A360917 11 | 11 17 24 30 37 44 50 57 64 71 77 86 ... %e A360917 12 | 12 18 26 33 40 47 55 62 70 77 86 92 ... %e A360917 ... %Y A360917 Main diagonal is A331968. %Y A360917 Cf. A360199, A360915, A360916 (maximum induced paths), A360920. %K A360917 nonn,tabl %O A360917 1,2 %A A360917 _Andrew Howroyd_, Feb 26 2023