A307835 Number of partitions of n into 3 distinct squarefree parts.

0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 2, 2, 3, 5, 4, 4, 5, 9, 8, 8, 9, 12, 11, 11, 12, 16, 15, 15, 17, 21, 19, 18, 20, 25, 24, 22, 28, 33, 32, 28, 33, 40, 37, 35, 40, 50, 47, 42, 48, 58, 56, 48, 56, 65, 66, 57, 63, 73, 73, 65, 70, 82, 80, 74, 81, 92, 90, 80, 92, 102, 102, 88, 104, 116, 116

Offset: 0

Author

Ilya Gutkovskiy, May 01 2019

Keywords

• nonn

Examples

			a(15) = 4 because we have [11, 3, 1], [10, 3, 2], [7, 6, 2] and [7, 5, 3].
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A005117, A008683, A087188, A098236, A125688, A307815, A307825.

Programs

Mathematica

Table[Count[IntegerPartitions[n, {3}], _?(And[UnsameQ @@ #, AllTrue[#, SquareFreeQ[#] &]] &)], {n, 0, 75}]

Formula

a(n) = [x^n y^3] Product_{k>=1} (1 + mu(k)^2*y*x^k).