A308960 Sum of the largest parts in the partitions of n into 7 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 5, 13, 19, 34, 40, 58, 77, 118, 139, 194, 232, 324, 385, 508, 576, 775, 883, 1133, 1274, 1630, 1821, 2262, 2525, 3093, 3450, 4153, 4563, 5494, 6067, 7155, 7842, 9283, 10177, 11860, 12928, 15051, 16466, 18969, 20543, 23705, 25820

Offset

0,9

Links

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

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 * (n-i-j-k-l-m-o), where mu is the Möbius function (A008683).

a(n) = A308953(n) - A308954(n) - A308955(n) - A308956(n) - A308957(n) - A308958(n) - A308959(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[(n-i-j-k-l-m-o) * 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, A308958, A308959.

Sequence in context: A222114 A308845 A308911 * A326452 A326532 A326637

Adjacent sequences: A308957 A308958 A308959 * A308961 A308962 A308963

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 03 2019

Status

approved