A308762 - OEIS

%I #28 Jun 25 2019 03:59:38

%S 0,0,0,0,1,1,2,3,6,6,10,11,16,16,22,23,35,38,51,57,75,76,94,99,125,

%T 128,158,162,208,209,242,251,311,317,376,390,467,478,548,553,672,682,

%U 784,801,957,957,1096,1101,1284,1294,1471,1469,1725,1717,1917,1918

%N Sum of the third 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 * j, where mu is the Möbius function (A008683).

%F a(n) = A308783(n) - A308768(n) - A308769(n) - A308770(n).

%t Table[Sum[Sum[Sum[j * 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, A308767, A308768, A308769, A308770, A308783.

%K nonn

%O 0,7

%A _Wesley Ivan Hurt_, Jun 23 2019