A308911 Sum of the largest parts in the partitions of n into 6 squarefree parts.

0, 0, 0, 0, 0, 0, 1, 2, 5, 5, 13, 19, 34, 38, 55, 74, 110, 125, 173, 206, 292, 333, 433, 493, 662, 729, 929, 1034, 1323, 1441, 1770, 1955, 2403, 2598, 3096, 3376, 4066, 4360, 5121, 5566, 6584, 7064, 8183, 8832, 10326, 11021, 12626, 13592, 15701, 16743, 18957

Offset: 0

Author

Wesley Ivan Hurt, Jun 29 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A008683, A308902, A308903, A308906, A308907, A308908, A308909, A308910.

Programs

Mathematica

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

Formula

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

a(n) = A308903(n) - A308906(n) - A308907(n) - A308908(n) - A308909(n) - A308910(n).