%I #7 Jun 25 2019 04:00:05

%S 0,0,0,0,1,1,3,4,8,8,14,15,24,25,41,45,64,64,85,93,120,123,159,172,

%T 221,222,279,291,375,386,472,494,610,612,734,745,901,899,1075,1067,

%U 1297,1272,1493,1490,1765,1757,2046,2076,2398,2408,2743,2774,3187,3177

%N Sum of the second largest parts of the partitions of n into 4 squarefree parts.

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

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

%F a(n) = A308783(n) - A308768(n) - A308762(n) - A308770(n).

%t Table[Sum[Sum[Sum[i * MoebiusMu[k]^2*MoebiusMu[j]^2*MoebiusMu[i]^2* MoebiusMu[n - i - j - k]^2, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]

%Y Cf. A008683, A308762, A308767, A308768, A308770, A308783.

%K nonn

%O 0,7

%A _Wesley Ivan Hurt_, Jun 23 2019