A184250 Number of strings of numbers x(i=1..n) in 0..2 with sum i^3*x(i) equal to n^3*2

1, 1, 1, 2, 1, 3, 5, 4, 17, 18, 28, 74, 109, 183, 491, 759, 1118, 2986, 4480, 7212, 17741, 28158, 45715, 100767, 166088, 267176, 577835, 953092, 1574492, 3267846, 5292990, 8871119, 17707401, 29095912, 48748589, 95299744, 156993030, 260741932