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

Author

Yi Yang, Oct 01 2022

Keywords

• nonn
• walk
• hard
• more

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.

Examples

			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
		

Links

• Yi Yang, The longest road in a square grid (see 2nd post with a C++ program that generates a(2)-a(19)).

Crossrefs

Cf. A331986, A357234.

Extensions

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