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

1,3

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.

Links

Table of n, a(n) for n=1..23.

Dave Budd, Collinear cells in hexagon polyominoes

Dave Budd, Optimized version for exhaustive proof of A377756

Example

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

Prog

(Python) # See links

Crossrefs

Cf. A000228, A378015.

Sequence in context: A112572 A089325 A110593 * A049368 A152733 A215455

Adjacent sequences: A377753 A377754 A377755 * A377757 A377758 A377759

Keyword

nonn,fini,full,new

Author

Dave Budd, Nov 06 2024

Status

approved