A331986 Number of snake-like polyominoes with the maximum possible number of unit squares in an n X n square.

1, 4, 8, 84, 56, 136, 52, 216, 16, 1504, 2352, 1152, 1344, 123216, 82432, 11008, 308992

Offset: 1

Author

Alain Goupil, Feb 03 2020

Keywords

• nonn
• walk
• hard
• more

Comments

The maximum possible number of unit squares is given by A331968(n).

Equivalently, a(n) is the number of maximum length paths without chords in the n X n grid graph. A path without chords is an induced subgraph that is a path.

For n > 1, a(n) is a multiple of 4 since a solution can have at most one symmetry considering rotations and reflections. - Andrew Howroyd, Feb 04 2020

Examples

			For n = 4 the number of snake-like polyominoes with 11 cells is 84.
		

Links

• Eric Weisstein's World of Mathematics, Grid Graph

Crossrefs

Main diagonal of A360916.

Cf. A331968, A059525 (connected induced subgraphs), A099155.

Cf. A332920 (non-isomorphic snakes), A332921 (symmetric snakes).

Extensions

a(15) from Andrew Howroyd, Feb 04 2020

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