A382954 Number of ways to partition distinct prime numbers into three disjoint sets such that the sum of each set equals n.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, 3, 2, 8, 1, 1, 4, 0, 14, 9, 1, 4, 7, 16, 26, 31, 17, 3, 19, 39, 54, 20, 62, 9, 41, 96, 89, 62, 66, 34, 59, 197, 241, 289, 69, 124, 184, 133, 481, 440, 148, 225, 394, 709, 808, 984, 555, 414, 799

Offset: 0

Author

Seiichi Manyama, Apr 10 2025

Keywords

• nonn

Comments

Conjecture: a(n) > 0 for n > 35.

Examples

			a(29) = 3: [29; 19, 7, 3; 13, 11, 5], [29; 17, 7, 3, 2; 13, 11, 5], [29; 17, 7, 5; 13, 11, 3, 2].
a(30) = 2: [23, 7; 19, 11; 17, 13], [23, 5, 2; 19, 11; 17, 13].
		

Crossrefs

Cf. A000607, A258281, A382871.

Formula

a(n) = 1/6 * [(x*y*z)^n] Product_{p prime} (1 + x^p + y^p + z^p) for n > 0.