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%I #20 Nov 16 2024 13:39:51
%S 1,0,1,0,2,1,0,4,2,1,0,3,15,3,1,0,5,50,23,3,1,0,1,171,126,30,4,1,0,1,
%T 506,710,187,39,4,1,0,1,1459,3520,1268,270,48,5,1,0,1,3792,16617,7703,
%U 1948,364,59,5,1,0,1,9292,72870,45099,12885,2840,488,70,6,1
%N Triangle read by rows: T(n,k) = number of free hexagonal polyominoes with n cells, where the maximum number of cells on any lattice line is k. The term "lattice line" here means a line running through the cell centers and midpoints of their sides.
%C The row sums are the total number of free hexagonal polyominoes with n cells.
%H Dave Budd, <a href="https://github.com/daveisagit/oeis/blob/main/hex_grid/connected_nodes.py">Python code for a hex lattice</a>
%e | k
%e n | 1 2 3 4 5 6 7 8 9 10 Total
%e ---------------------------------------------------------------------------------------
%e 1 | 1 1
%e 2 | 0 1 1
%e 3 | 0 2 1 3
%e 4 | 0 4 2 1 7
%e 5 | 0 3 15 3 1 22
%e 6 | 0 5 50 23 3 1 82
%e 7 | 0 1 171 126 30 4 1 333
%e 8 | 0 1 506 710 187 39 4 1 1448
%e 9 | 0 1 1459 3520 1268 270 48 5 1 6572
%e 10 | 0 1 3792 16617 7703 1948 364 59 5 1 30490
%e The T(4,2)=4 hexagon polyominoes are:
%e # # # # # #
%e # # # # # # # #
%e # #
%Y Row sums are A000228.
%Y Cf. A377941, A378015.
%K nonn,tabl
%O 1,5
%A _Dave Budd_, Nov 14 2024