A326452 Sum of the largest parts of the partitions of n into 8 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 5, 13, 19, 34, 40, 60, 80, 121, 147, 208, 253, 350, 417, 563, 651, 863, 1002, 1299, 1484, 1888, 2151, 2678, 3046, 3729, 4211, 5110, 5721, 6868, 7670, 9142, 10146, 11996, 13319, 15606, 17251, 20084, 22173, 25708, 28253, 32522

Offset

0,10

Links

Table of n, a(n) for n=0..50.

Index entries for sequences related to partitions

Formula

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

a(n) = A326444(n) - A326445(n) - A326446(n) - A326447(n) - A326448(n) - A326449(n) - A326450(n) - A326451(n).

Mathematica

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

Crossrefs

Cf. A008683, A326443, A326444, A326445, A326446, A326447, A326448, A326449, A326450, A326451.

Sequence in context: A308845 A308911 A308960 * A326532 A326637 A303355

Adjacent sequences: A326449 A326450 A326451 * A326453 A326454 A326455

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 06 2019

Status

approved