

A268311


Number of free polyominoes that form a continuous path of edge joined cells spanning an n X n square in both dimensions.


8




OFFSET

1,2


COMMENTS

This idea originated from the water retention model for mathematical surfaces and is identical to the concept of a "lake." A lake is body of water that has dimensions of (n2) X (n2) when the square size is nxn. All other bodies of water are "ponds".
Iwan Jensen with his transfer matrix algorithm provided the number of symmetrically redundant solutions. Walter Trump enumerated the symmetrically unique solutions.


LINKS

Table of n, a(n) for n=1..8.
Craig Knecht, Polyominoe enumeration
Craig Knecht, Connective polyominoes 3x3
Wikipedia, Connective Polyominoes 4x4
Wikipedia, Connective Polyominoes 5x5
Wikipedia, Connective polyominoes with 4 symaxis
Wikipedia, Pond larger than a lake
Wikipedia, Water Retention on Mathematical Surfaces


EXAMPLE

The cells with value one show the smallest possible lake in this 4x4 square.
1 1 1 1
0 0 0 1
0 0 0 1
0 0 0 1


CROSSREFS

Cf. A054247 (all unique water retention patterns for an n X n square).
Sequence in context: A122551 A136524 A213984 * A137887 A232310 A028365
Adjacent sequences: A268308 A268309 A268310 * A268312 A268313 A268314


KEYWORD

nonn,more


AUTHOR

Craig Knecht, Jan 31 2016


STATUS

approved



