A024681 a(n) = number of ways p(n) is a sum of 3 odd nonprimes r,s,t satisfying 9 <= r < s < t.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 4, 5, 4, 6, 10, 9, 11, 10, 16, 13, 23, 21, 24, 32, 34, 40, 44, 47, 48, 50, 60, 69, 72, 80, 78, 88, 104, 118, 117, 131, 127, 136, 149, 157, 164, 177, 192, 201, 212, 213, 223, 236, 277, 279, 294, 290, 342, 358, 367, 398, 385, 409, 441