Obtained from the polyominoes of A056780 by discarding the polyominoes that contain 2x2 sub-blocks of 4 cells. One may call this the Tatami version of the free rectangular polyominoes.
This might also be considered a well-defined (or corrected?) version of A002369.
Table of n, a(n) for n=1..11.
from the A056780(4) = 9 polyominoes the one with the 2x2 bounding box is not counted, giving a(4)=8.
From the A056780(5)=21 polyominoes 2 are not counted:
LL and LL
Cf. A056780, A002369.
Sequence in context: A041281 A078343 A148038 * A148039 A148040 A148041
Adjacent sequences: A326298 A326299 A326300 * A326302 A326303 A326304
R. J. Mathar, Oct 17 2019