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%I #39 Feb 27 2023 11:16:08
%S 1,4,8,84,56,136,52,216,16,1504,2352,1152,1344,123216,82432,11008,
%T 308992
%N Number of snake-like polyominoes with the maximum possible number of unit squares in an n X n square.
%C The maximum possible number of unit squares is given by A331968(n).
%C Equivalently, a(n) is the number of maximum length paths without chords in the n X n grid graph. A path without chords is an induced subgraph that is a path.
%C For n > 1, a(n) is a multiple of 4 since a solution can have at most one symmetry considering rotations and reflections. - _Andrew Howroyd_, Feb 04 2020
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%e For n = 4 the number of snake-like polyominoes with 11 cells is 84.
%Y Main diagonal of A360916.
%Y Cf. A331968, A059525 (connected induced subgraphs), A099155.
%Y Cf. A332920 (non-isomorphic snakes), A332921 (symmetric snakes).
%K nonn,walk,hard,more
%O 1,2
%A _Alain Goupil_, Feb 03 2020
%E a(15) from _Andrew Howroyd_, Feb 04 2020
%E a(16)-a(17) from _Yi Yang_, Oct 03 2022