A378015 Triangle read by rows: T(n,k) = number of free hexagonal polyominoes with n cells, where the maximum number of collinear cell centers on any line in the plane is k.

1, 0, 1, 0, 2, 1, 0, 4, 2, 1, 0, 2, 16, 3, 1, 0, 3, 52, 23, 3, 1, 0, 0, 169, 129, 30, 4, 1, 0, 0, 477, 740, 187, 39, 4, 1, 0, 0, 1245, 3729, 1274, 270, 48, 5, 1, 0, 0, 2750, 17578, 7785, 1948, 364, 59, 5, 1, 0, 0, 5380, 75827, 46045, 12895, 2840, 488, 70, 6, 1

Offset

1,5

Comments

The row sums are the total number of free hexagon polyominoes with n cells.

Links

Table of n, a(n) for n=1..66.

Dave Budd, Python code for a hex lattice.

Example

   |  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      2     16      3      1                                             22
 6 |       0      3     52     23      3      1                                      82
 7 |       0      0    169    129     30      4      1                              333
 8 |       0      0    477    740    187     39      4      1                      1448
 9 |       0      0   1245   3729   1274    270     48      5      1               6572
10 |       0      0   2750  17578   7785   1948    364     59      5      1       30490
The T(5,2)=2 hexagon polyominoes are:
 #          #   #
#   #        # #
 # #        #

Crossrefs

Cf. A000228 (row sums).

Cf. A377942 (similar collinear cell constraint for square polyominoes).

Cf. A377756 (specific case for the cumulative value for k<=3 i.e. T(n,1)+T(n,2)+T(n,3) ).

Cf. A378014 (collinear cell constraint applied only to cells on lattice lines).

Sequence in context: A062296 A249343 A369206 * A378014 A355756 A140649

Adjacent sequences: A378012 A378013 A378014 * A378016 A378017 A378018

Keyword

nonn,tabl

Author

Dave Budd, Nov 14 2024

Status

approved