A377942 - OEIS

%I #34 Feb 14 2025 17:28:05

%S 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 200,77,25,4,1,0,0,86,678,369,114,33,4,1,0,0,78,2177,1590,593,170,41,

%U 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 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 The row sum is the number of free polyominoes with n cells.

%H John Mason, <a href="/A377942/b377942.txt">Table of n, a(n) for n = 1..153</a>

%H Dave Budd, <a href="https://github.com/daveisagit/oeis/blob/main/square_lattice/connected_nodes.py">Python code for a square lattice</a>

%e    |  k

%e n  |       1      2      3      4      5      6      7      8      9     10

%e ----------------------------------------------------------------------------

%e  1 |       1

%e  2 |       0      1

%e  3 |       0      1      1

%e  4 |       0      2      2      1

%e  5 |       0      0      9      2      1

%e  6 |       0      0     18     13      3      1

%e  7 |       0      0     37     48     19      3      1

%e  8 |       0      0     62    200     77     25      4      1

%e  9 |       0      0     86    678    369    114     33      4      1

%e 10 |       0      0     78   2177   1590    593    170     41      5      1

%e ...

%e From _John Mason_, Feb 14 2025: (Start)

%e 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  O

%e  OO

%e   OO

%e (End)

%Y Row sums are A000105.

%Y Cf. A377941.

%K nonn,tabl

%O 1,8

%A _Dave Budd_, Nov 11 2024

%E More terms from _Pontus von Brömssen_, Nov 12 2024