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

John Mason, Table of n, a(n) for n = 1..153

Dave Budd, Python code for a square lattice

Example

   |  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)

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