A308958 Sum of the third largest parts in the partitions of n into 7 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 6, 8, 14, 17, 25, 30, 44, 50, 72, 83, 115, 136, 184, 213, 278, 321, 409, 463, 579, 650, 807, 900, 1089, 1215, 1462, 1610, 1926, 2133, 2520, 2772, 3258, 3586, 4195, 4587, 5327, 5847, 6780, 7376, 8513, 9283, 10639, 11538, 13168

Offset

0,10

Links

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

Index entries for sequences related to partitions

Formula

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

a(n) = A308953(n) - A308954(n) - A308955(n) - A308956(n) - A308957(n) - A308959(n) - A308960(n).

Mathematica

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

Crossrefs

Cf. A008683, A308952, A308953, A308954, A308955, A308956, A308957, A308959, A308960.

Sequence in context: A308909 A369356 A378790 * A326450 A326530 A326635

Adjacent sequences: A308955 A308956 A308957 * A308959 A308960 A308961

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 03 2019

Status

approved