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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.

Original entry on oeis.org

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

Offset: 1

Talmon Silver, Dec 19 2020

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 polyominoes 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.

			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.

John Mason, Explanation of a(5)
Talmon Silver, Computing a(6)
Talmon Silver, Programs