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A331986
Number of snake-like polyominoes with the maximum possible number of unit squares in an n X n square.
6
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
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
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