A308955 - OEIS

%I #6 Jul 03 2019 06:12:36

%S 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,

%T 168,185,229,255,311,342,414,459,547,593,711,782,911,987,1159,1270,

%U 1467,1580,1823,1990,2276,2441,2799,3035,3435,3686,4177,4505,5062

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

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F 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).

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

%t 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}]

%Y Cf. A008683, A308952, A308953, A308954, A308956, A308957, A308958, A308959, A308960.

%K nonn

%O 0,10

%A _Wesley Ivan Hurt_, Jul 03 2019