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 (n-2) X (n-2) when the square size is n X n. 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
Craig Knecht, Polyominoes enumeration
Craig Knecht, Connective polyominoes 3x3
R. J. Mathar, Corrigendum to "Polyomino Enumeration Results (Parkin et al, SIAM Fall Meeting 1967)" viXra:1905.0474 (2019)
R. Parkin, L. J. Lander, and D. R. Parkin, Polyomino Enumeration Results, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy) page 9 (incorrect at n=15).
Wikipedia, Connective Polyominoes 4x4
Wikipedia, Connective Polyominoes 5x5
Wikipedia, Connective polyominoes with 4 sym-axis
Wikipedia, Pond larger than a lake
Wikipedia, Water Retention on Mathematical Surfaces
EXAMPLE
The cells with value 1 show the smallest possible lake in this 4 X 4 square:
1 1 1 1
0 0 0 1
0 0 0 1
0 0 0 1
a(3)=24 = 6+7+7+3+1: There fit 6 5-ominoes in a 3x3 square, 7 6-ominoes in a 3x3 square, 7 7-ominoes in a 3x3 square, 3 8-ominoes in a 3x3 square, a 1 9-omino in a 3x3 square. - R. J. Mathar, Jun 07 2020
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Craig Knecht, Jan 31 2016
EXTENSIONS
a(6) corrected. Craig Knecht, May 25 2020
STATUS
approved