A377756 - OEIS

%I #29 Dec 03 2024 12:41:14

%S 1,1,3,6,18,55,169,477,1245,2750,5380,8989,12674,14741,13928,10297,

%T 6185,2910,1012,289,69,12,2

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

%C 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.

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

%H Dave Budd, <a href="https://github.com/daveisagit/oeis/blob/main/hex_grid/connected_nodes.py">Collinear cells in hexagon polyominoes</a>

%H Dave Budd, <a href="https://github.com/daveisagit/collinear-polyominoes/blob/main/src/A377756.py">Optimized version for exhaustive proof of A377756</a>

%e For n=23, the 2 hexagon polyominoes are:

%e             @ @                      @

%e            @                    @     @

%e     @       @                    @ @   @

%e      @ @     @          @           @ @

%e @   @       @            @ @           @

%e  @   @       @          @   @           @

%e   @ @         @              @ @       @

%e      @     @ @                  @   @ @

%e       @ @ @                      @ @

%o (Python) # See links

%Y Cf. A000228, A378015.

%K nonn,fini,full

%O 1,3

%A _Dave Budd_, Nov 06 2024