A326523 Sum of all the parts in the partitions of n into 9 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 22, 24, 52, 70, 120, 144, 221, 288, 418, 500, 714, 858, 1173, 1392, 1850, 2184, 2862, 3304, 4263, 4950, 6231, 7136, 8910, 10234, 12530, 14256, 17316, 19684, 23673, 26640, 31816, 35826, 42355, 47388, 55755, 62284, 72662

Offset

0,10

Links

Table of n, a(n) for n=0..47.

Index entries for sequences related to partitions

Formula

a(n) = 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)} mu(q)^2 * mu(p)^2 * mu(o)^2 * mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l-m-o-p-q)^2, where mu is the Möbius function (A008683).

a(n) = n * A326522(n).

a(n) = A326524(n) + A326525(n) + A326526(n) + A326527(n) + A326528(n) + A326529(n) + A326530(n) + A326531(n) + A326532(n).

Mathematica

Table[n*Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[MoebiusMu[q]^2 * MoebiusMu[p]^2 * MoebiusMu[o]^2 * MoebiusMu[m]^2 * MoebiusMu[l]^2 * MoebiusMu[k]^2 * MoebiusMu[j]^2 * MoebiusMu[i]^2*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, 80}]

Crossrefs

Cf. A008683, A326522, A326524, A326525, A326526, A326527, A326528, A326529, A326530, A326531, A326532.

Sequence in context: A214425 A260184 A109463 * A061410 A309485 A228378

Adjacent sequences: A326520 A326521 A326522 * A326524 A326525 A326526

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 11 2019

Status

approved