A280316 Sum of squares of parts of the partitions of 2n into two squarefree parts.

2, 18, 44, 124, 108, 372, 398, 886, 888, 1560, 1642, 2778, 2098, 3440, 2810, 5618, 5350, 9766, 6934, 12382, 9744, 17448, 11112, 20440, 12728, 24050, 19508, 26610, 25270, 36108, 28950, 41020, 31974, 56038, 42490, 74484, 51668, 77210, 52810, 87970, 57074, 105804, 68972

Offset: 1

Author

Wesley Ivan Hurt, Dec 31 2016

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A008683, A280226, A280320, A280322.

Programs

Maple

with(numtheory): A280316:=n->add((i^2+(2*n-i)^2) * mobius(i)^2 * mobius(2*n-i)^2, i=1..n): seq(A280316(n), n=1..100);

Formula

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

a(n) = A280320(n) + A280322(n).