A294097 Number of partitions of 2n into two parts such that both parts are either squarefree or nonsquarefree.

1, 2, 2, 4, 2, 5, 3, 7, 5, 8, 6, 10, 6, 10, 6, 12, 9, 17, 8, 16, 9, 18, 9, 19, 10, 21, 14, 20, 15, 22, 14, 23, 14, 27, 17, 33, 18, 30, 16, 30, 16, 33, 17, 35, 23, 34, 22, 36, 22, 39, 24, 40, 25, 49, 24, 44, 25, 46, 25, 47, 25, 50, 32, 46, 31, 48, 30, 49, 30

Offset

1,2

Links

Table of n, a(n) for n=1..69.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=1..n} [A008966(i) = A008966(2n-i)], where [] is the Iverson bracket.

Mathematica

Table[Sum[KroneckerDelta[MoebiusMu[k]^2, MoebiusMu[2 n - k]^2], {k, n}], {n, 80}]

Crossrefs

Cf. A008966, A294098.

Sequence in context: A125296 A366707 A366708 * A233520 A243271 A232245

Adjacent sequences: A294094 A294095 A294096 * A294098 A294099 A294100

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 22 2017

Status

approved