A377942 Triangle read by rows: T(n,k) = number of free polyominoes with n cells, where the maximum number of collinear cell centers on any line in the plane is k.

1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 0, 9, 2, 1, 0, 0, 18, 13, 3, 1, 0, 0, 37, 48, 19, 3, 1, 0, 0, 62, 200, 77, 25, 4, 1, 0, 0, 86, 678, 369, 114, 33, 4, 1, 0, 0, 78, 2177, 1590, 593, 170, 41, 5, 1, 0, 0, 61, 6280, 6739, 2774, 928, 234, 51, 5, 1, 0, 0, 34, 17187, 27153, 12851, 4597, 1387, 323, 61, 6, 1

Offset

1,8

Comments

The row sum is the number of free 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      0      9      2      1                                        12
 6 |       0      0     18     13      3      1                                 35
 7 |       0      0     37     48     19      3      1                         108
 8 |       0      0     62    200     77     25      4      1                  369
 9 |       0      0     86    678    369    114     33      4      1          1285
10 |       0      0     78   2177   1590    593    170     41      5      1   4655
...

Crossrefs

Row sums are A000105.

Cf. A377941.

Sequence in context: A334493 A074080 A359440 * A347687 A368948 A368579

Adjacent sequences: A377939 A377940 A377941 * A377943 A377944 A377945

Keyword

nonn,tabl

Author

Dave Budd, Nov 11 2024

Extensions

More terms from Pontus von Brömssen, Nov 12 2024

Status

approved