OFFSET
1,2
LINKS
Nikolai Beluhov, Snake paths in king and knight graphs, arXiv:2301.01152 [math.CO], 2023.
Elijah Beregovsky, Illustration of initial terms.
Eric Weisstein's World of Mathematics, Grid Graph.
Wikipedia, Induced path.
FORMULA
a(n) <= A331968(n)+1.
a(n) = 2*n^2/3 + O(n) (Beluhov 2023). - Pontus von Brömssen, Jan 30 2023
EXAMPLE
For 2 <= n <= 6, a longest induced cycle is the one going around the border of the grid, so a(n) = 4*(n-1).
Longest induced cycles for 6 <= n <= 8:
X X X X X X X X X X X X X X X X X X X X X
X . . . . X X . . . . . X X . . . . . . X
X . . . . X X . X X X . X X . X X X . X X
X . . . . X X . X . X . X X . X . X . X .
X . . . . X X . X . X . X X . X . X . X X
X X X X X X X . X . X . X X . X . X . . X
X X X . X X X X . X . X . . X
X X X . X X X X
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Pontus von Brömssen, Sep 25 2022
EXTENSIONS
a(9)-a(12) from Elijah Beregovsky, Nov 24 2022
a(13) from Elijah Beregovsky, Nov 25 2022
a(14)-a(17) from Andrew Howroyd, Feb 26 2023
STATUS
approved