A326631 Sum of the seventh 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, 8, 10, 15, 19, 28, 33, 45, 55, 73, 86, 113, 132, 171, 198, 250, 288, 359, 411, 504, 578, 700, 798, 961, 1090, 1306, 1477, 1752, 1976, 2338, 2625, 3080, 3457, 4029, 4508, 5228, 5831, 6733, 7490, 8594, 9547

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

a(n) = A326627(n) - A326628(n) - A326629(n) - A326630(n) - A326632(n) - A326633(n) - A326634(n) - A326635(n) - A326636(n) - A326637(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[o * 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, A326632, A326633, A326634, A326635, A326636, A326637.

Sequence in context: A027337 A364892 A325434 * A260894 A193146 A240486

Adjacent sequences: A326628 A326629 A326630 * A326632 A326633 A326634

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 14 2019

Status

approved