A377941 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.

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

Offset: 1

Author

Dave Budd, Nov 11 2024

Keywords

• nonn
• tabl

Comments

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

Examples

			   | k
n  |       1      2      3      4      5      6      7      8      9     10  Total
----------------------------------------------------------------------------------
 1 |       1                                                                     1
 2 |       0      1                                                              1
 3 |       0      1      1                                                       2
 4 |       0      2      2      1                                                5
 5 |       0      1      8      2      1                                        12
 6 |       0      1     17     13      3      1                                 35
 7 |       0      1     39     45     19      3      1                         108
 8 |       0      1     79    182     77     25      4      1                  369
 9 |       0      1    162    607    363    114     33      4      1          1285
10 |       0      1    301   2004   1539    593    170     41      5      1   4655
 ...
The T(4,2)=2 polyominoes are:
  * *      * *
  * *        * *
		

Links

• John Mason, Table of n, a(n) for n = 1..153 (17 rows)
• Dave Budd, Python code for a square lattice

Crossrefs

Row sums are A000105.

Cf. A377942.

Extensions

More terms from Pontus von Brömssen, Nov 12 2024