A367439 a(n) is the degree of the polyomino with binary code A246521(n+1) in the polyomino graph PG(n) defined in A367435.

0, 0, 1, 1, 4, 3, 4, 3, 2, 10, 8, 3, 9, 10, 9, 8, 9, 10, 8, 4, 2, 15, 28, 15, 12, 12, 10, 17, 14, 19, 20, 15, 14, 15, 13, 18, 20, 9, 14, 13, 17, 4, 12, 16, 18, 11, 9, 10, 15, 22, 19, 10, 19, 14, 16, 3, 36, 36, 35, 31, 28, 30, 36, 22, 29, 37, 16, 11, 28, 13, 24

Offset: 1

Author

Pontus von Brömssen, Nov 18 2023

Keywords

• nonn
• tabf

Comments

Number of free polyominoes that can be made from the polyomino with binary code A246521(n+1) by moving one of its cells (not counting itself), where the intermediate (the set of cells remaining when the cell to be moved is detached) is required to be a (connected) polyomino.

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

Examples

			As an irregular triangle:
   0;
   0;
   1, 1;
   4, 3, 4, 3,  2;
  10, 8, 3, 9, 10, 9, 8, 9, 10, 8, 4, 2;
  ...
For n = 8, A246521(8+1) = 30 is the binary code of the S-tetromino. By moving one cell of the S-tetromino, we can obtain the L, O, and T tetrominoes (but not the I tetromino), so a(8) = 3.
		

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..6473 (rows 1..10).
• Index entries for sequences related to polyominoes.

Crossrefs

Cf. A000105, A246521, A367126, A367435, A367437 (row maxima), A367438, A367443.

Formula

a(n) <= A367126(n).