

A331986


Number of snakelike polyominoes with the maximum possible number of unit squares in an n X n square.


3



1, 4, 8, 84, 56, 136, 52, 216, 16, 1504, 2352, 1152, 1344, 123216, 82432
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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..15.
Eric Weisstein's World of Mathematics, Grid Graph


EXAMPLE

For n = 4 the number of snakelike polyominoes with 11 cells is 84.


CROSSREFS

Cf. A331968, A059525 (connected induced subgraphs), A099155.
Cf. A332920 (nonisomorphic snakes), A332921 (symmetric snakes).
Sequence in context: A090254 A222287 A120281 * A057974 A071277 A273060
Adjacent sequences: A331983 A331984 A331985 * A331987 A331988 A331989


KEYWORD

nonn,walk,more


AUTHOR

Alain Goupil, Feb 03 2020


EXTENSIONS

a(15) from Andrew Howroyd, Feb 04 2020


STATUS

approved



