A339848 Number of distinct free polyominoes that fit in an n X n square but are not a proper sub-polyomino of any polyomino that fits in the square.

1, 1, 1, 1, 3, 6, 16, 27, 44, 70

Offset

1,5

Comments

A polyomino A is a proper sub-polyomino of B if one or more cells can be added to A to form B.

Except for the n X n polyomino that fills the square all of the other polyominos must have their edges aligned at an angle to the sides of the square.

This counts the minimum subset of polyominoes needed to produce A268427 - that sequence counts the sub-polyominoes of this sequence.

Links

Table of n, a(n) for n=1..10.

John Mason, Explanation of a(5)

Talmon Silver, Computing a(6)

Talmon Silver, Programs

Example

For n=1, 2, 3, 4 the only polyominoes are the n X n polyominoes. Thus, a(1)=a(2)=a(3)=a(4)=1.
For n=5 and n=6 all of the other polyominoes are shown in the links.

Crossrefs

Cf. A268427.

Sequence in context: A144538 A130596 A280730 * A321409 A151954 A032247

Adjacent sequences: A339845 A339846 A339847 * A339849 A339850 A339851

Keyword

nonn,more

Author

Talmon Silver, Dec 19 2020

Status

approved