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

1,5

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.

Links

Pontus von Brömssen, Table of n, a(n) for n = 1..6473 (rows 1..10).

Index entries for sequences related to polyominoes.

Formula

a(n) <= A367126(n).

Example

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.

Crossrefs

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

Sequence in context: A106049 A367914 A238234 * A367126 A136627 A108171

Adjacent sequences: A367436 A367437 A367438 * A367440 A367441 A367442

Keyword

nonn,tabf

Author

Pontus von Brömssen, Nov 18 2023

Status

approved