A309485 Sum of the squarefree parts of the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 22, 32, 61, 90, 149, 208, 321, 455, 653, 877, 1244, 1649, 2238, 2921, 3882, 4980, 6502, 8205, 10523, 13182, 16611, 20545, 25621, 31406, 38648, 46962, 57251, 68982, 83338, 99595, 119319, 141732, 168430, 198685, 234663, 275171

Offset

0,10

Links

David A. Corneth, Table of n, a(n) for n = 0..9999

Index entries for sequences related to partitions

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} (q * mu(q)^2 + p * mu(p)^2 + o * mu(o)^2 + m * mu(m)^2 + l * mu(l)^2 + k * mu(k)^2 + j * mu(j)^2 + i * mu(i)^2 + (n-i-j-k-l-m-o-p-q) * mu(n-i-j-k-l-m-o-p-q)^2), where mu is the Möbius function (A008683).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(i * MoebiusMu[i]^2 + j * MoebiusMu[j]^2 + k * MoebiusMu[k]^2 + l * MoebiusMu[l]^2 + m * MoebiusMu[m]^2 + o * MoebiusMu[o]^2 + p * MoebiusMu[p]^2 + q * MoebiusMu[q]^2 + (n - i - j - k - l - m - o - p - q) * MoebiusMu[n - i - j - k - l - m - o - p - q]^2), {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o,  Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

Crossrefs

Cf. A008683, A309463, A309478, A309479, A309480, A309481, A309482, A309484, A309485, A309486.

Sequence in context: A109463 A326523 A061410 * A228378 A326464 A174042

Adjacent sequences: A309482 A309483 A309484 * A309486 A309487 A309488

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 04 2019

Status

approved