%I #10 May 08 2023 14:58:44
%S 4,4,4,4,8,4,4,10,10,4,4,12,12,12,4,4,14,14,14,14,4,4,16,16,16,16,16,
%T 4,4,18,20,18,18,20,18,4,4,20,22,24,20,24,22,20,4,4,22,24,26,28,28,26,
%U 24,22,4,4,24,28,28,30,32,30,28,28,24,4,4,26,30,32,32,36,36,32,32,30,26,4
%N Array read by antidiagonals: T(m,n) is the length of the longest induced cycle in the grid graph P_m X P_n.
%C All terms are even since the grid graph is bipartite.
%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>.
%F T(m,n) = T(n,m).
%F T(m,n) = 2*m*n/3 + O(m+n) (Beluhov 2023, Proposition 3). - _Pontus von Brömssen_, May 08 2023
%e Array begins:
%e ==========================================
%e m\n| 2 3 4 5 6 7 8 9 10 11 12 ...
%e -----+------------------------------------
%e 2 | 4 4 4 4 4 4 4 4 4 4 4 ...
%e 3 | 4 8 10 12 14 16 18 20 22 24 26 ...
%e 4 | 4 10 12 14 16 20 22 24 28 30 32 ...
%e 5 | 4 12 14 16 18 24 26 28 32 36 38 ...
%e 6 | 4 14 16 18 20 28 30 32 36 42 44 ...
%e 7 | 4 16 20 24 28 32 36 40 44 48 52 ...
%e 8 | 4 18 22 26 30 36 40 46 50 56 60 ...
%e 9 | 4 20 24 28 32 40 46 50 56 62 68 ...
%e 10 | 4 22 28 32 36 44 50 56 62 70 74 ...
%e 11 | 4 24 30 36 42 48 56 62 70 76 82 ...
%e 12 | 4 26 32 38 44 52 60 68 74 82 90 ...
%e ...
%Y Main diagonal is A357357.
%Y Cf. A360196, A360913, A360917, A360920.
%K nonn,tabl
%O 2,1
%A _Andrew Howroyd_, Feb 26 2023