A326635 Sum of the third largest parts of the partitions of n into 10 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 6, 8, 14, 17, 27, 34, 50, 59, 86, 105, 145, 176, 238, 286, 378, 451, 584, 690, 876, 1022, 1280, 1487, 1824, 2104, 2557, 2932, 3536, 4030, 4803, 5463, 6478, 7327, 8633, 9751, 11420, 12854, 14985, 16822, 19536, 21874

Offset

0,13

Links

Table of n, a(n) for n=0..53.

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

a(n) = A326627(n) - A326628(n) - A326629(n) - A326630(n) - A326631(n) - A326632(n) - A326633(n) - A326634(n) - A326636(n) - A326637(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[j * 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, A326632, A326633, A326634, A326636, A326637.

Sequence in context: A308958 A326450 A326530 * A212214 A089426 A167934

Adjacent sequences: A326632 A326633 A326634 * A326636 A326637 A326638

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 14 2019

Status

approved