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.

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

Table of n, a(n) for n=1..16.

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

Cf. A331986, A357234.

Sequence in context: A110956 A298446 A364563 * A205012 A254120 A356778

Adjacent sequences: A357513 A357514 A357515 * A357517 A357518 A357519

Keyword

nonn,walk,hard,more

Author

Yi Yang, Oct 01 2022

Extensions

a(14)-a(16) from Andrew Howroyd, Feb 28 2023

Status

approved