%N The number of rectangular free polyominoes with n cells where no 4 cells meet at a point.
%C 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.
%C This might also be considered a well-defined (or corrected?) version of A002369.
%e from the A056780(4) = 9 polyominoes the one with the 2x2 bounding box is not counted, giving a(4)=8.
%e From the A056780(5)=21 polyominoes 2 are not counted:
%e LL and LL
%e LL LLL
%Y Cf. A056780, A002369.
%A _R. J. Mathar_, Oct 17 2019