A308955 Sum of the sixth largest parts in the partitions of n into 7 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 9, 11, 14, 17, 25, 29, 39, 43, 58, 67, 85, 93, 120, 136, 168, 185, 229, 255, 311, 342, 414, 459, 547, 593, 711, 782, 911, 987, 1159, 1270, 1467, 1580, 1823, 1990, 2276, 2441, 2799, 3035, 3435, 3686, 4177, 4505, 5062

Offset

0,10

Links

Table of n, a(n) for n=0..55.

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

a(n) = A308953(n) - A308954(n) - A308956(n) - A308957(n) - A308958(n) - A308959(n) - A308960(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[m * 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, A308956, A308957, A308958, A308959, A308960.

Sequence in context: A337823 A051630 A050045 * A098386 A326447 A326527

Adjacent sequences: A308952 A308953 A308954 * A308956 A308957 A308958

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 03 2019

Status

approved