%I #9 Jun 25 2019 03:59:50

%S 0,0,0,0,1,1,2,2,4,4,6,6,8,8,11,11,15,15,19,20,25,24,30,30,37,36,44,

%T 43,53,52,60,60,71,69,80,80,93,92,106,104,122,119,135,134,155,152,172,

%U 172,194,192,213,212,239,234,257,256,290,281,308,305,343,336

%N Number of 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, where mu is the Möbius function (A008683).

%F a(n) = A308783(n)/n.

%t Table[Sum[Sum[Sum[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, A308783.

%K nonn

%O 0,7

%A _Wesley Ivan Hurt_, Jun 23 2019