A326632 Sum of the sixth largest parts of the partitions of n into 10 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 9, 11, 16, 21, 31, 37, 51, 61, 83, 99, 129, 150, 197, 229, 288, 332, 417, 479, 589, 676, 830, 950, 1150, 1310, 1588, 1802, 2148, 2431, 2897, 3264, 3843, 4322, 5067, 5684, 6604, 7380, 8557, 9538, 10961, 12198

Offset

0,13

Links

Table of n, a(n) for n=0..55.

Index entries for sequences related to partitions

Formula

a(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 * m, where mu is the Möbius function (A008683).

a(n) = A326627(n) - A326628(n) - A326629(n) - A326630(n) - A326631(n) - A326633(n) - A326634(n) - A326635(n) - A326636(n) - A326637(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[m * 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, A326627, A326628, A326629, A326630, A326631, A326633, A326634, A326635, A326636, A326637.

Sequence in context: A098386 A326447 A326527 * A240206 A229816 A099574

Adjacent sequences: A326629 A326630 A326631 * A326633 A326634 A326635

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 14 2019

Status

approved