A048017 Number of nonempty subsets of {1,2,...,n} in which exactly 1/3 of the elements are <= (n-2)/3.

0, 0, 0, 0, 6, 10, 15, 45, 77, 126, 322, 570, 975, 2325, 4213, 7425, 17061, 31421, 56511, 126763, 236203, 431098, 950818, 1787346, 3298527, 7184421, 13598053, 25314061, 54604081, 103918153, 194810143, 416990563, 797154723, 1502994133