A048072 Number of nonempty subsets of {1,2,...,n} in which exactly 1/3 of the elements are <= (n+2)/3.

0, 0, 1, 2, 6, 13, 21, 45, 91, 154, 322, 645, 1125, 2325, 4651, 8301, 17061, 34123, 61915, 126763, 253527, 465746, 950818, 1901637, 3527109, 7184421, 14368843, 26855641, 54604081, 109208163, 205390163, 416990563, 833981127