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A360914 Number of maximum induced cycles in the n X n grid graph.

%I A360914 #8 Feb 16 2025 08:34:04
%S A360914 0,1,1,7,90,1398,23,2100,6840,2912,416,1344,102198,1643968,42592,
%T A360914 48128,1120128
%N A360914 Number of maximum induced cycles in the n X n grid graph.
%C A360914 A maximum induced cycle is an induced cycle of longest length.
%H A360914 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>.
%e A360914 The a(3) = 1 unique cycle of longest length is:
%e A360914    O O O
%e A360914    O   O
%e A360914    O O O
%e A360914 .
%e A360914 The a(4) = 7 maximum induced cycles have length 12 and are the following subgraphs with their rotations and reflections.
%e A360914    O O O O     O O O     O O O
%e A360914    O     O   O O   O   O O   O
%e A360914    O     O   O     O   O   O O
%e A360914    O O O O   O O O O   O O O
%Y A360914 Main diagonal of A360913.
%Y A360914 Cf. A297664, A357357 (lengths).
%K A360914 nonn,more
%O A360914 1,4
%A A360914 _Andrew Howroyd_, Feb 26 2023