A048094 Number of nonempty subsets of {1,2,...,n} in which exactly 1/3 of the elements are <= sqrt(n).

0, 0, 1, 2, 6, 13, 25, 45, 91, 175, 322, 570, 975, 1617, 2607, 7425, 12753, 21385, 35065, 56302, 88638, 136986, 208050, 310840, 1251606, 1973706, 3065931, 4694921, 7092211, 10575635, 15576535, 22674015, 32637675, 46480475