A378014 Triangle read by rows: T(n,k) = number of free hexagonal polyominoes with n cells, where the maximum number of cells on any lattice line is k. The term "lattice line" here means a line running through the cell centers and midpoints of their sides.

1, 0, 1, 0, 2, 1, 0, 4, 2, 1, 0, 3, 15, 3, 1, 0, 5, 50, 23, 3, 1, 0, 1, 171, 126, 30, 4, 1, 0, 1, 506, 710, 187, 39, 4, 1, 0, 1, 1459, 3520, 1268, 270, 48, 5, 1, 0, 1, 3792, 16617, 7703, 1948, 364, 59, 5, 1, 0, 1, 9292, 72870, 45099, 12885, 2840, 488, 70, 6, 1

Offset: 1

Author

Dave Budd, Nov 14 2024

Keywords

• nonn
• tabl

Comments

The row sums are the total number of free hexagonal 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      2      1                                                            3
 4 |       0      4      2      1                                                     7
 5 |       0      3     15      3      1                                             22
 6 |       0      5     50     23      3      1                                      82
 7 |       0      1    171    126     30      4      1                              333
 8 |       0      1    506    710    187     39      4      1                      1448
 9 |       0      1   1459   3520   1268    270     48      5      1               6572
10 |       0      1   3792  16617   7703   1948    364     59      5      1       30490
The T(4,2)=4 hexagon polyominoes are:
  #         #        #   #      # #
   # #       # #      # #      # #
      #     #
		

Links

• Dave Budd, Python code for a hex lattice

Crossrefs

Row sums are A000228.

Cf. A377941, A378015.