A308956 Sum of the fifth largest parts in the partitions of n into 7 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 6, 10, 12, 16, 20, 30, 34, 46, 52, 71, 80, 103, 115, 149, 167, 211, 236, 298, 332, 410, 457, 559, 619, 742, 814, 981, 1078, 1269, 1384, 1633, 1786, 2072, 2246, 2607, 2839, 3267, 3524, 4050, 4379, 4970, 5350, 6076, 6555

Offset

0,10

Links

Table of n, a(n) for n=0..54.

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

a(n) = A308953(n) - A308954(n) - A308955(n) - A308957(n) - A308958(n) - A308959(n) - A308960(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[l * 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, A308957, A308958, A308959, A308960.

Sequence in context: A285908 A060988 A359744 * A309834 A326448 A326528

Adjacent sequences: A308953 A308954 A308955 * A308957 A308958 A308959

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 03 2019

Status

approved