A059451 Number of ways n can be written as the sum of two numbers whose binary expansions have even numbers of zeros; also number of ways n can be written as the sum of two numbers whose binary expansions have odd numbers of zeros.

0, 1, 0, 1, 1, 1, 1, 2, 0, 2, 2, 1, 3, 2, 1, 3, 2, 2, 4, 3, 1, 4, 3, 3, 4, 4, 2, 4, 5, 3, 5, 5, 2, 5, 6, 3, 7, 6, 1, 7, 6, 4, 8, 6, 3, 7, 7, 5, 8, 7, 4, 9, 5, 6, 11, 6, 6, 9, 6, 7, 11, 8, 5, 10, 8, 7, 12, 8, 7, 11, 7, 9, 12, 10, 6, 12, 9, 7, 17, 9, 6, 13, 10, 9, 15, 12, 5, 14, 12, 9, 16, 11, 9, 14, 11