A048084 Number of nonempty subsets of {1,2,...,n} in which exactly 2/3 of the elements are <= (n+3)/3.

0, 0, 1, 2, 3, 9, 12, 15, 40, 51, 63, 175, 220, 270, 759, 945, 1155, 3311, 4102, 5005, 14547, 17955, 21875, 64275, 79116, 96288, 285413, 350568, 426303, 1272601, 1560449, 1896279, 5694129, 6972339, 8468163, 25554035, 31253950