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%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,new
%O 1,3
%A _Dave Budd_, Nov 06 2024