A048029 Number of nonempty subsets of {1,2,...,n} in which exactly 2/3 of the elements are <= (n-3)/3.

0, 0, 0, 0, 0, 0, 0, 0, 7, 8, 9, 27, 30, 33, 121, 138, 156, 520, 595, 675, 2255, 2600, 2975, 9877, 11445, 13167, 43510, 50625, 58513, 192801, 225093, 261165, 858199, 1004754, 1169505, 3834655, 4500210, 5252445, 17189667, 20214327