

A331968


Maximum number of unit squares of a snakelike polyomino in an n X n square box.


11



1, 3, 7, 11, 17, 24, 33, 42, 53, 64, 77, 92, 107, 123, 142, 162, 182
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OFFSET

1,2


COMMENTS

These are similar to the snakeinthebox problem for the hypercube Q_n (See A099155).
The number of solutions is given by A331986(n).
Equivalently, a(n) is the maximum number of vertices in a path without chords in the n X n grid graph. A path without chords is an induced subgraph that is a path.
These numbers are part of the result of a computer program that counts the snakelike polyominoes in a rectangle of given size b X h by their length.
a(16) >= 161.


LINKS



FORMULA

For n > 2: a(n) >= 2*floor(n/3)*(2n3*floor(n/3)2)+5.  Elijah Beregovsky, May 11 2020


EXAMPLE

For n=4, the maximum length of a snakelike polyomino that fits in a square of side 4 is 11 and there are 84 such snakes.
Maximumlength snakes for n = 1 to 4 are shown below.
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,hard,more


AUTHOR



EXTENSIONS

a(16)a(17) from Yi Yang, Oct 03 2022


STATUS

approved



