This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378014 #20 Nov 16 2024 13:39:51 %S A378014 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 A378014 506,710,187,39,4,1,0,1,1459,3520,1268,270,48,5,1,0,1,3792,16617,7703, %U A378014 1948,364,59,5,1,0,1,9292,72870,45099,12885,2840,488,70,6,1 %N A378014 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 A378014 The row sums are the total number of free hexagonal polyominoes with n cells. %H A378014 Dave Budd, <a href="https://github.com/daveisagit/oeis/blob/main/hex_grid/connected_nodes.py">Python code for a hex lattice</a> %e A378014 | k %e A378014 n | 1 2 3 4 5 6 7 8 9 10 Total %e A378014 --------------------------------------------------------------------------------------- %e A378014 1 | 1 1 %e A378014 2 | 0 1 1 %e A378014 3 | 0 2 1 3 %e A378014 4 | 0 4 2 1 7 %e A378014 5 | 0 3 15 3 1 22 %e A378014 6 | 0 5 50 23 3 1 82 %e A378014 7 | 0 1 171 126 30 4 1 333 %e A378014 8 | 0 1 506 710 187 39 4 1 1448 %e A378014 9 | 0 1 1459 3520 1268 270 48 5 1 6572 %e A378014 10 | 0 1 3792 16617 7703 1948 364 59 5 1 30490 %e A378014 The T(4,2)=4 hexagon polyominoes are: %e A378014 # # # # # # %e A378014 # # # # # # # # %e A378014 # # %Y A378014 Row sums are A000228. %Y A378014 Cf. A377941, A378015. %K A378014 nonn,tabl %O A378014 1,5 %A A378014 _Dave Budd_, Nov 14 2024