A308767 Number of partitions of n into 4 squarefree parts.

0, 0, 0, 0, 1, 1, 2, 2, 4, 4, 6, 6, 8, 8, 11, 11, 15, 15, 19, 20, 25, 24, 30, 30, 37, 36, 44, 43, 53, 52, 60, 60, 71, 69, 80, 80, 93, 92, 106, 104, 122, 119, 135, 134, 155, 152, 172, 172, 194, 192, 213, 212, 239, 234, 257, 256, 290, 281, 308, 305, 343, 336

Offset

0,7

Links

Table of n, a(n) for n=0..61.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k)^2, where mu is the Möbius function (A008683).

a(n) = A308783(n)/n.

Mathematica

Table[Sum[Sum[Sum[MoebiusMu[k]^2*MoebiusMu[j]^2*MoebiusMu[i]^2*MoebiusMu[n - i - j - k]^2, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]

Crossrefs

Cf. A008683, A308783.

Sequence in context: A052928 A346663 A137501 * A353504 A345419 A285999

Adjacent sequences: A308764 A308765 A308766 * A308768 A308769 A308770

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 23 2019

Status

approved