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

1,2

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

Links

Table of n, a(n) for n=1..17.

Eric Weisstein's World of Mathematics, Grid Graph

Example

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

Crossrefs

Main diagonal of A360916.

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

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

Sequence in context: A090254 A222287 A120281 * A057974 A071277 A336795

Adjacent sequences: A331983 A331984 A331985 * A331987 A331988 A331989

Keyword

nonn,walk,hard,more

Author

Alain Goupil, Feb 03 2020

Extensions

a(15) from Andrew Howroyd, Feb 04 2020

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

Status

approved