%I #26 Feb 14 2025 10:49:57

%S 1,0,1,0,1,1,0,2,2,1,0,1,8,2,1,0,1,17,13,3,1,0,1,39,45,19,3,1,0,1,79,

%T 182,77,25,4,1,0,1,162,607,363,114,33,4,1,0,1,301,2004,1539,593,170,

%U 41,5,1,0,1,589,6139,6361,2764,928,234,51,5,1,0,1,1141,18278,25072,12733,4597,1387,323,61,6,1

%N Triangle read by rows: T(n,k) = number of free polyominoes with n cells, where the maximum number of cells in any row or column is k.

%C The row sum are the total number of polyominoes with n cells.

%H John Mason, <a href="/A377941/b377941.txt">Table of n, a(n) for n = 1..153</a> (17 rows)

%H Dave Budd, <a href="https://github.com/daveisagit/oeis/blob/main/square_lattice/connected_nodes.py">Python code for a square lattice</a>

%e | k

%e n | 1 2 3 4 5 6 7 8 9 10 Total

%e ----------------------------------------------------------------------------------

%e 1 | 1 1

%e 2 | 0 1 1

%e 3 | 0 1 1 2

%e 4 | 0 2 2 1 5

%e 5 | 0 1 8 2 1 12

%e 6 | 0 1 17 13 3 1 35

%e 7 | 0 1 39 45 19 3 1 108

%e 8 | 0 1 79 182 77 25 4 1 369

%e 9 | 0 1 162 607 363 114 33 4 1 1285

%e 10 | 0 1 301 2004 1539 593 170 41 5 1 4655

%e ...

%e The T(4,2)=2 polyominoes are:

%e * * * *

%e * * * *

%Y Row sums are A000105.

%Y Cf. A377942.

%K nonn,tabl

%O 1,8

%A _Dave Budd_, Nov 11 2024

%E More terms from _Pontus von Brömssen_, Nov 12 2024