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A357516
Number of snake-like polyominoes in an n X n square that start at the NW corner and end at the SE corner and have the maximum length.
3
1, 2, 6, 20, 2, 64, 44, 512, 28, 4, 64, 520, 480, 6720, 43232, 14400
OFFSET
1,2
COMMENTS
The maximum length is given by A357234(n).
If the lower bounds of A357234(n) are tight, then a(14)-a(19) are 6720, 43232, 14400, 226560, 1646080, 403712.
For n > 1, a(n) is even since for every solution there is also the symmetrical solution reflected in the main diagonal.
LINKS
Yi Yang, The longest road in a square grid (see 2nd post with a C++ program that generates a(2)-a(19)).
EXAMPLE
For n = 5, there are 2 such snakes shown as follows:
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
Sequence in context: A110956 A298446 A364563 * A205012 A254120 A356778
KEYWORD
nonn,walk,hard,more
AUTHOR
Yi Yang, Oct 01 2022
EXTENSIONS
a(14)-a(16) from Andrew Howroyd, Feb 28 2023
STATUS
approved