A151678 a(n) = sum_{k >= 0} binomial(wt(n+k),2*k), where wt() = A000120().

1, 1, 2, 1, 2, 2, 4, 1, 2, 2, 4, 2, 4, 5, 7, 1, 2, 2, 4, 2, 4, 5, 7, 2, 4, 5, 7, 5, 8, 12, 11, 1, 2, 2, 4, 2, 4, 5, 7, 2, 4, 5, 7, 5, 8, 12, 11, 2, 4, 5, 7, 5, 8, 12, 11, 5, 8, 12, 12, 12, 17, 26, 16, 1, 2, 2, 4, 2, 4, 5, 7, 2, 4, 5, 7, 5, 8, 12, 11, 2, 4, 5, 7, 5, 8, 12, 11, 5, 8, 12, 12, 12, 17, 26, 16