Offsetting squares (array/grid) without intersecting lines

Hi all,

I want to do something so seemingly easy it drives me crazy it does not work. I Want to create an offset distributions of squares like the first image. So it should be with an offset either by making a square grid or arraying a square, rotating 45 degrees and then I tried both scaling and offset. With a triangular or hexagonal grid, no problem to achieve this, but in the ways i tried the squares are not scaling from their center point. I tried manually moving them to scale from the center rather than the corner but this also didn’t work.

Anyone a smart way to do so? (see screenshot for 3 failed, or at least incomplete attempts)

I might have been unclear in my problem statement, which is that with the square pattern, the intersecting lines of the offsets do not disappear.

If i use scale, the squares are not scaling independently from their respective centers, but as a whole grid from the origin.

I want to use the separate squares created with the offset.