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A307835
Number of partitions of n into 3 distinct squarefree parts.
8
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
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}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 01 2019
STATUS
approved