OFFSET
1,3
REFERENCES
Thomas Dawson, Échecs Féeriques, L'Échiquier, volume 2, issue 2, 1930; issue 3, 1931.
Donald E. Knuth, The Art of Computer Programming, Volume 4B, Combinatorial Algorithms, Part 2, Addison-Wesley, 2023. See exercise 7.2.2.1-172 and its solution.
LINKS
Nikolai Beluhov, Snake paths in king and knight graphs, arXiv:2301.01152 [math.CO], 2023.
Eric Weisstein's World of Mathematics, Knight Graph.
Wikipedia, Induced path
FORMULA
a(n) >= A165143(n) - 1 for n >= 3.
a(n) <= (4*(n^2+3*n-2)-1)/7 for n >= 4. - Elijah Beregovsky, Dec 22 2022
a(n) = n^2/2 + O(n) (Beluhov 2023). - Pontus von Brömssen, Jan 30 2023
EXAMPLE
Longest paths for 3 <= n <= 7:
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, Oct 01 2022
STATUS
approved