A048018 Number of nonempty subsets of {1,2,...,n} in which exactly 2/3 of the elements are <= (n-2)/3.

0, 0, 0, 0, 0, 0, 0, 6, 7, 8, 24, 27, 30, 105, 121, 138, 450, 520, 595, 1939, 2255, 2600, 8456, 9877, 11445, 37122, 43510, 50625, 164025, 192801, 225093, 728409, 858199, 1004754, 3248322, 3834655, 4500210, 14536951, 17189667