A294103 Sum of the differences of the larger and smaller parts in the partitions of 2n into two squarefree parts or two nonsquarefree parts.

0, 2, 4, 12, 4, 24, 20, 54, 40, 72, 70, 114, 62, 116, 62, 182, 126, 292, 134, 330, 182, 412, 190, 460, 202, 468, 380, 518, 490, 632, 462, 692, 458, 890, 562, 1184, 638, 1088, 590, 1206, 590, 1430, 678, 1556, 986, 1578, 952, 1772, 1032, 1876, 1214, 1986, 1326

Offset

1,2

Links

Table of n, a(n) for n=1..53.

Index entries for sequences related to partitions

Formula

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

Mathematica

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

Crossrefs

Cf. A008966, A294097.

Sequence in context: A070314 A075554 A365000 * A137369 A334766 A336847

Adjacent sequences: A294100 A294101 A294102 * A294104 A294105 A294106

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 22 2017

Status

approved