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A360919 Number of maximum induced trees in the n X n grid graph.

%I A360919 #11 Feb 16 2025 08:34:04
%S A360919 1,4,10,32,22,4120,488,65864,166,1296,872,37652512,678412,1858036816,
%T A360919 337856
%N A360919 Number of maximum induced trees in the n X n grid graph.
%C A360919 A maximum induced tree is an induced tree of greatest size.
%H A360919 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>.
%e A360919 The a(3) = 10 maximum induced trees are the following subgraphs and their rotations and reflections.
%e A360919    O O O    O O O    O O O
%e A360919    O        O   O      O
%e A360919    O O O      O O    O O O
%e A360919 .
%e A360919 The a(4) = 32 maximum induced trees are the following subgraphs and their rotations and reflections.
%e A360919     O O O O    O O O      O O O O    O O   O
%e A360919     O     O    O   O O      O   O      O O O
%e A360919     O O   O    O O   O    O O   O    O O   O
%e A360919     O   O O    O   O O    O   O O    O   O O
%Y A360919 Main diagonal of A360918.
%Y A360919 Cf. A360203 (induced trees), A360921 (maximum sizes).
%K A360919 nonn,more
%O A360919 1,2
%A A360919 _Andrew Howroyd_, Feb 26 2023