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 A377942 #34 Feb 14 2025 17:28:05 %S A377942 1,0,1,0,1,1,0,2,2,1,0,0,9,2,1,0,0,18,13,3,1,0,0,37,48,19,3,1,0,0,62, %T A377942 200,77,25,4,1,0,0,86,678,369,114,33,4,1,0,0,78,2177,1590,593,170,41, %U A377942 5,1,0,0,61,6280,6739,2774,928,234,51,5,1,0,0,34,17187,27153,12851,4597,1387,323,61,6,1 %N A377942 Triangle read by rows: T(n,k) = number of free polyominoes with n cells, where the maximum number of collinear cell centers on any line in the plane is k. %C A377942 The row sum is the number of free polyominoes with n cells. %H A377942 John Mason, <a href="/A377942/b377942.txt">Table of n, a(n) for n = 1..153</a> %H A377942 Dave Budd, <a href="https://github.com/daveisagit/oeis/blob/main/square_lattice/connected_nodes.py">Python code for a square lattice</a> %e A377942 | k %e A377942 n | 1 2 3 4 5 6 7 8 9 10 %e A377942 ---------------------------------------------------------------------------- %e A377942 1 | 1 %e A377942 2 | 0 1 %e A377942 3 | 0 1 1 %e A377942 4 | 0 2 2 1 %e A377942 5 | 0 0 9 2 1 %e A377942 6 | 0 0 18 13 3 1 %e A377942 7 | 0 0 37 48 19 3 1 %e A377942 8 | 0 0 62 200 77 25 4 1 %e A377942 9 | 0 0 86 678 369 114 33 4 1 %e A377942 10 | 0 0 78 2177 1590 593 170 41 5 1 %e A377942 ... %e A377942 From _John Mason_, Feb 14 2025: (Start) %e A377942 The first difference with A377941 occurs at n=5 when the following polyomino has maximum number of row or column cells = 2, but there are 3 cells on a 45 degree diagonal. %e A377942 O %e A377942 OO %e A377942 OO %e A377942 (End) %Y A377942 Row sums are A000105. %Y A377942 Cf. A377941. %K A377942 nonn,tabl %O A377942 1,8 %A A377942 _Dave Budd_, Nov 11 2024 %E A377942 More terms from _Pontus von Brömssen_, Nov 12 2024