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

1,8

Comments

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

Links

Table of n, a(n) for n=1..78.

Dave Budd, Python code for a square lattice

Example

   | 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:
  * *      * *
  * *        * *

Crossrefs

Row sums are A000105.

Cf. A377942.

Sequence in context: A355755 A141335 A133624 * A030110 A083570 A287407

Adjacent sequences: A377938 A377939 A377940 * A377942 A377943 A377944

Keyword

nonn,tabl

Author

Dave Budd, Nov 11 2024

Extensions

More terms from Pontus von Brömssen, Nov 12 2024

Status

approved