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A331986 Number of snake-like 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 (list; graph; refs; listen; history; text; internal format)
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 snake-like polyominoes with 11 cells is 84.

CROSSREFS

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

Cf. A332920 (non-isomorphic 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

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Last modified September 21 14:54 EDT 2020. Contains 337272 sequences. (Running on oeis4.)