A377756 Number of free hexagonal polyominoes with n cells with at most 3 collinear cell centers on any line in the plane.

1, 1, 3, 6, 18, 55, 169, 477, 1245, 2750, 5380, 8989, 12674, 14741, 13928, 10297, 6185, 2910, 1012, 289, 69, 12, 2

Offset: 1

Author

Dave Budd, Nov 06 2024

Keywords

• nonn
• fini
• full

Comments

a(n) is the number of connected planer graphs with n nodes, where the nodes lie on a triangular lattice grid and no more than 3 nodes are collinear over the underlying plane.

a(n) is the sum of columns 1-3 in A378015, the n-th term = Sum(T(n,k)) for k<=3.

Examples

			For n=23, the 2 hexagon polyominoes are:
            @ @                      @
           @                    @     @
    @       @                    @ @   @
     @ @     @          @           @ @
@   @       @            @ @           @
 @   @       @          @   @           @
  @ @         @              @ @       @
     @     @ @                  @   @ @
      @ @ @                      @ @
		

Links

• Dave Budd, Collinear cells in hexagon polyominoes
• Dave Budd, Optimized version for exhaustive proof of A377756

Crossrefs

Cf. A000228, A378015.

Programs

Python

# See links