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 A378015 #9 Nov 16 2024 13:39:45 %S A378015 1,0,1,0,2,1,0,4,2,1,0,2,16,3,1,0,3,52,23,3,1,0,0,169,129,30,4,1,0,0, %T A378015 477,740,187,39,4,1,0,0,1245,3729,1274,270,48,5,1,0,0,2750,17578,7785, %U A378015 1948,364,59,5,1,0,0,5380,75827,46045,12895,2840,488,70,6,1 %N A378015 Triangle read by rows: T(n,k) = number of free hexagonal polyominoes with n cells, where the maximum number of collinear cell centers on any line in the plane is k. %C A378015 The row sums are the total number of free hexagon polyominoes with n cells. %H A378015 Dave Budd, <a href="https://github.com/daveisagit/oeis/blob/main/hex_grid/connected_nodes.py">Python code for a hex lattice</a>. %e A378015 | k %e A378015 n | 1 2 3 4 5 6 7 8 9 10 Total %e A378015 --------------------------------------------------------------------------------------- %e A378015 1 | 1 1 %e A378015 2 | 0 1 1 %e A378015 3 | 0 2 1 3 %e A378015 4 | 0 4 2 1 7 %e A378015 5 | 0 2 16 3 1 22 %e A378015 6 | 0 3 52 23 3 1 82 %e A378015 7 | 0 0 169 129 30 4 1 333 %e A378015 8 | 0 0 477 740 187 39 4 1 1448 %e A378015 9 | 0 0 1245 3729 1274 270 48 5 1 6572 %e A378015 10 | 0 0 2750 17578 7785 1948 364 59 5 1 30490 %e A378015 The T(5,2)=2 hexagon polyominoes are: %e A378015 # # # %e A378015 # # # # %e A378015 # # # %Y A378015 Cf. A000228 (row sums). %Y A378015 Cf. A377942 (similar collinear cell constraint for square polyominoes). %Y A378015 Cf. A377756 (specific case for the cumulative value for k<=3 i.e. T(n,1)+T(n,2)+T(n,3) ). %Y A378015 Cf. A378014 (collinear cell constraint applied only to cells on lattice lines). %K A378015 nonn,tabl %O A378015 1,5 %A A378015 _Dave Budd_, Nov 14 2024