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%I #4 Jan 19 2021 21:04:25
%S 0,0,0,0,1,1,0,2,4,5,2,1,7,10,4,11,23,22,16,26,35,31,28,28,52,48,43,
%T 49,80,73,34,58,105,107,70,99,195,157,89,159,258,227,164,238,374,327,
%U 251,282,480,404,306,306,539,481,402,290,566,528,472,352,630,582,495,500,766,648,598,546,1033,733,772,616,1428,873,952,938,1515,1111,1028,1239,1742
%N Number of partitions of n into 4 parts such that the sum of the smallest two parts and the sum of the largest two parts are both squarefree.
%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)/3)} mu(k+j)^2 * mu(n-j-k)^2, where mu is the Möbius function (A008683).
%t Table[Sum[Sum[Sum[MoebiusMu[k + j]^2*MoebiusMu[n - j - k]^2, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 80}]
%Y Cf. A008683 (mu).
%K nonn
%O 0,8
%A _Wesley Ivan Hurt_, Jan 19 2021
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