A309458 Number of squarefree parts in the partitions of n into 6 parts.

0, 0, 0, 0, 0, 0, 6, 6, 12, 17, 29, 40, 62, 77, 109, 139, 186, 229, 299, 361, 454, 547, 672, 797, 967, 1132, 1352, 1574, 1850, 2131, 2486, 2841, 3276, 3723, 4256, 4805, 5461, 6125, 6910, 7721, 8655, 9621, 10739, 11883, 13193, 14550, 16083, 17669, 19460

Offset

0,7

Links

Table of n, a(n) for n=0..48.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_(i=j..floor((n-j-k-l-m)/2)} (mu(i)^2 + mu(j)^2 + mu(k)^2 + mu(l)^2 + mu(m)^2 + mu(n-i-j-k-l-m)^2), where mu is the Möbius function (A008683).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[MoebiusMu[i]^2 + MoebiusMu[j]^2 + MoebiusMu[k]^2 + MoebiusMu[l]^2 + MoebiusMu[m]^2 + MoebiusMu[n - i - j - k - l - m]^2, {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 50}]

Crossrefs

Cf. A008683.

Sequence in context: A122223 A046625 A315787 * A029682 A014201 A315788

Adjacent sequences: A309455 A309456 A309457 * A309459 A309460 A309461

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 03 2019

Status

approved