# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a268311
Showing 1-1 of 1

%I A268311 #52 Mar 21 2024 21:03:57
%S A268311 1,2,24,1051,238048,195284973,577169894573,6200686124225191
%N A268311 Number of free polyominoes that form a continuous path of edge joined cells spanning an n X n square in both dimensions.
%C A268311 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".
%C A268311 Iwan Jensen with his transfer matrix algorithm provided the number of symmetrically redundant solutions. _Walter Trump_ enumerated the symmetrically unique solutions.
%H A268311 Craig Knecht, <a href="/A268311/a268311.pdf">Polyominoes enumeration</a>
%H A268311 Craig Knecht, <a href="/A268311/a268311.png">Connective polyominoes 3x3</a>
%H A268311 R. J. Mathar, <a href="http://www.vixra.org/abs/1905.0474">Corrigendum to "Polyomino Enumeration Results (Parkin et al, SIAM Fall Meeting 1967)"</a> viXra:1905.0474 (2019)
%H A268311 R. Parkin, L. J. Lander, and D. R. Parkin, <a href="/A000104/a000104.pdf">Polyomino Enumeration Results</a>, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy) page 9 (incorrect at n=15).
%H A268311 Wikipedia, <a href="https://en.wikipedia.org/wiki/File:Connective_polyominoes.jpeg">Connective Polyominoes 4x4</a>
%H A268311 Wikipedia, <a href="https://en.wikipedia.org/wiki/File:Connective_polyominoes_5x5.jpeg">Connective Polyominoes 5x5</a>
%H A268311 Wikipedia, <a href="https://en.wikipedia.org/wiki/File:Connective_polyominoes_with_4_sym-axis.jpg">Connective polyominoes with 4 sym-axis</a>
%H A268311 Wikipedia, <a href="https://en.wikipedia.org/wiki/File:Pond_larger_than_a_lake.png">Pond larger than a lake</a>
%H A268311 Wikipedia, <a href="http://en.wikipedia.org/wiki/Water retention on mathematical surfaces">Water Retention on Mathematical Surfaces</a>
%H A268311 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>
%e A268311 The cells with value 1 show the smallest possible lake in this 4 X 4 square:
%e A268311 1 1 1 1
%e A268311 0 0 0 1
%e A268311 0 0 0 1
%e A268311 0 0 0 1
%e A268311 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
%Y A268311 Cf. A054247 (all unique water retention patterns). Diagonal of A268371.
%Y A268311 Cf. A259088.
%K A268311 nonn,more
%O A268311 1,2
%A A268311 _Craig Knecht_, Jan 31 2016
%E A268311 a(6) corrected. _Craig Knecht_, May 25 2020

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE