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

0,10

Links

Table of n, a(n) for n=0..75.

Index entries for sequences related to partitions

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A049879 A053812 A177865 * A341651 A017828 A140087

Adjacent sequences: A307832 A307833 A307834 * A307836 A307837 A307838

Keyword

nonn

Author

Ilya Gutkovskiy, May 01 2019

Status

approved