A308907 Sum of the fifth largest parts in the partitions of n into 6 squarefree parts.

0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 6, 10, 10, 14, 18, 26, 28, 37, 41, 57, 62, 77, 87, 113, 122, 152, 170, 213, 230, 279, 307, 376, 402, 471, 516, 622, 661, 768, 830, 978, 1041, 1194, 1282, 1492, 1586, 1804, 1932, 2217, 2340, 2632, 2815, 3195, 3380, 3780, 4026

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, A308908, A308909, A308910, A308911.

Programs

Mathematica

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

a(n) = A308903(n) - A308906(n) - A308908(n) - A308909(n) - A308910(n) - A308911(n).