%I #9 Jan 29 2023 23:01:37
%S 0,8,94,1004,14864,334536,11546874,629381852,56094263348,
%T 8343512638896,2074276200162230,853966325494701152,
%U 578432462293854136504,646135466408339553958096,1200595044818176185884236342
%N Number of induced paths in the n X n grid graph.
%C Paths of length zero are not counted here.
%C Equivalently, a(n) is the number of snake-like polyominoes in an n X n square. Rotations, reflections and translations are counted separately.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Induced_path">Induced path</a>
%e The a(2) = 8 induced paths are:
%e O O O . . . . O O O O . . O O O
%e . . O . O O . O O . O O O O . O
%Y Main diagonal of A360199.
%Y Cf. A059525, A297664 (induced cycles), A331968, A331986 (of maximum length), A357516.
%K nonn,more
%O 1,2
%A _Andrew Howroyd_, Jan 29 2023