A048040 Number of nonempty subsets of {1,2,...,n} in which exactly 2/3 of the elements are <= (n+1)/3.

0, 0, 0, 0, 3, 4, 5, 15, 18, 21, 63, 76, 90, 270, 325, 385, 1155, 1390, 1651, 5005, 6027, 7175, 21875, 26348, 31416, 96288, 116010, 138510, 426303, 513729, 614019, 1896279, 2285569, 2734171, 8468163, 10208110, 12220780, 37941280