A326627 Sum of all the parts in the partitions of n into 10 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 11, 24, 26, 56, 75, 128, 153, 234, 304, 460, 546, 770, 943, 1296, 1550, 2054, 2430, 3220, 3770, 4830, 5642, 7168, 8283, 10302, 11935, 14688, 16872, 20482, 23439, 28360, 32226, 38430, 43602, 51876, 58455, 68816, 77503, 90816

Offset

0,11

Links

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

Index entries for sequences related to partitions

Formula

a(n) = n * Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} mu(r)^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-r)^2, where mu is the Möbius function (A008683).

a(n) = n * A326626(n).

a(n) = A326628(n) + A326629(n) + A326630(n) + A326631(n) + A326632(n) + A326633(n) + A326634(n) + A326635(n) + A326636(n) + A326637(n).

Mathematica

Table[n * Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[MoebiusMu[r]^2 * 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 - r]^2 , {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 50}]

Crossrefs

Cf. A008683, A326626, A326628, A326629, A326630, A326631, A326632, A326633, A326634, A326635, A326636, A326637.

Sequence in context: A173900 A214957 A367354 * A309486 A326588 A309357

Adjacent sequences: A326624 A326625 A326626 * A326628 A326629 A326630

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 14 2019

Status

approved