A294233 Number of partitions of n into two parts with smaller part nonsquarefree and larger part squarefree.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 2, 3, 1, 2, 2, 3, 1, 3, 3, 3, 1, 2, 3, 3, 1, 3, 3, 4, 0, 4, 5, 5, 2, 5, 6, 5, 2, 4, 6, 6, 2, 5, 7, 8, 2, 5, 6, 9, 4, 7, 7, 9, 4, 7, 8, 8, 4, 8, 9, 9, 3, 8, 8, 10, 1, 9, 9, 10, 3, 8, 10, 9, 4, 8, 11, 11, 3, 9

Offset

1,18

Links

Table of n, a(n) for n=1..85.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor(n/2)} (1 - mu(i)^2) * mu(n-i)^2, where mu is the Möbius function (A008683).

Mathematica

Table[Sum[(1 - MoebiusMu[k]^2) (MoebiusMu[n - k]^2), {k, Floor[n/2]}], {n, 80}]

Crossrefs

Cf. A008683, A008966, A294232.

Sequence in context: A283325 A353707 A318438 * A121884 A079087 A324920

Adjacent sequences: A294230 A294231 A294232 * A294234 A294235 A294236

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 25 2017

Status

approved