Is it possible to tile an equilateral integer-sided triangle with smaller equilateral integer-sided triangles, with no congruent triangles touching? This has been answered in the negative for the case that no like sizes repeat, I would like to know if it can be done with repeats but like sizes not touching, even at a corner.

Some more info: I've been running a computer search for such a tiling and just finished the side-47 triangle which took 109 hours. But just because a 'reachable' tiling is hard to find, one should not expect no tiling at all. In related "squaring the square" problems tilings have been known to crop up of squares well over 100 on a side.