A367443 - OEIS

%I #12 Apr 26 2024 20:33:18

%S 1,2,4,3,9,1,5,4,3,8,6,5,11,10,10,6,6,9,5,2,4,5,11,13,11,3,12,9,11,10,

%T 11,5,11,5,11,12,11,12,5,6,10,5,13,12,12,7,6,6,7,11,11,6,11,6,5,4,12,

%U 11,11,13,12,11,12,14,13,12,6,7,11,3,11,11,10,11

%N a(n) is the number of free polyominoes that can be obtained from the polyomino with binary code A246521(n+1) by adding one cell.

%C Can be read as an irregular triangle, whose m-th row contains A000105(m) terms, m >= 1.

%H Pontus von Brömssen, <a href="/A367443/b367443.txt">Table of n, a(n) for n = 1..6473</a> (rows 1..10).

%H <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.

%e As an irregular triangle:

%e   1;

%e   2;

%e   4, 3;

%e   9, 1, 5,  4,  3;

%e   8, 6, 5, 11, 10, 10, 6, 6, 9, 5, 2, 4;

%e   ...

%e For n = 5, the L tetromino, whose binary code is A246521(5+1) = 15, can be extended to 9 different free pentominoes, so a(5) = 9. (All possible ways to add one cell lead to different pentominoes.)

%e For n = 6, the square tetromino, whose binary code is A246521(6+1) = 23, can only be extended to the P pentomino by adding one cell, so a(6) = 1.

%Y Cf. A000105, A246521, A255890 (row minima), A367126, A367439, A367441.

%K nonn,tabf

%O 1,2

%A _Pontus von Brömssen_, Nov 18 2023