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%I #18 Dec 14 2022 09:49:45
%S 6,8,15,20,28,40,48,58,73,88,104,126
%N Length of the longest induced cycle in the n X n torus grid graph.
%C It is somewhat unclear how a(2) should be defined. If the 2 X 2 torus grid graph is considered to have multiple edges we have a(2) = 2 (a double edge between two nodes makes a 2-cycle), otherwise a(2) = 4.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Induced_path">Induced path</a>.
%F a(n) ~ 2*n^2/3.
%F a(n) <= A357359(n) + 1.
%e Longest induced cycles for 3 <= n <= 8:
%e X . X X . . X X . X . X X X X . . . X . X . X . X X . X . X X . X
%e X X . X X . . X . X X . X . X X X . X . X . X X . X . X X . X X .
%e . X X . X X . X X . X . X X . . X . X . X X . X . X X . X X . X .
%e . . X X . X . X X . X . . X X X X . X . X . . X X . X . X X
%e . X X . X . X X X . X . X . X . X X X . X . X X . X
%e . . . X X X . X . X X . X X . X X . X X .
%e . X X . X . X X X . X X . X .
%e . X X . X . X X
%Y Cf. A000937, A297669, A357357, A357359.
%K nonn,more
%O 3,1
%A _Pontus von Brömssen_, Sep 25 2022
%E a(9)-a(12) from _Elijah Beregovsky_, Dec 11 2022
%E a(13)-a(14) from _Elijah Beregovsky_, Dec 13 2022