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

Author

Dave Budd, Nov 11 2024

Keywords

• nonn
• tabl

Comments

The row sum is the number of free polyominoes with n cells.

Examples

			   |  k
n  |       1      2      3      4      5      6      7      8      9     10
----------------------------------------------------------------------------
 1 |       1
 2 |       0      1
 3 |       0      1      1
 4 |       0      2      2      1
 5 |       0      0      9      2      1
 6 |       0      0     18     13      3      1
 7 |       0      0     37     48     19      3      1
 8 |       0      0     62    200     77     25      4      1
 9 |       0      0     86    678    369    114     33      4      1
10 |       0      0     78   2177   1590    593    170     41      5      1
...
From _John Mason_, Feb 14 2025: (Start)
The first difference with A377941 occurs at n=5 when the following polyomino has maximum number of row or column cells = 2, but there are 3 cells on a 45 degree diagonal.
 O
 OO
  OO
(End)
		

Links

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

Crossrefs

Row sums are A000105.

Cf. A377941.

Extensions

More terms from Pontus von Brömssen, Nov 12 2024