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%I #5 Aug 03 2019 21:47:42
%S 0,0,0,0,0,0,0,0,8,8,16,23,39,54,84,113,165,214,294,377,504,634,820,
%T 1020,1292,1581,1966,2382,2920,3502,4233,5033,6021,7098,8404,9835,
%U 11548,13416,15631,18046,20879,23965,27545,31451,35949,40838,46426,52504,59406
%N Number of squarefree parts in the partitions of n into 8 parts.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} (mu(i)^2 + mu(j)^2 + mu(k)^2 + mu(l)^2 + mu(m)^2 + mu(o)^2 + mu(p)^2 + mu(n-i-j-k-l-m-o-p)^2), where mu is the Möbius function (A008683).
%t Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(MoebiusMu[i]^2 + MoebiusMu[j]^2 + MoebiusMu[k]^2 + MoebiusMu[l]^2 + MoebiusMu[m]^2 + MoebiusMu[o]^2 + MoebiusMu[p]^2 + MoebiusMu[n - i - j - k - l - m - o - p]^2), {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]
%Y Cf. A008683.
%K nonn
%O 0,9
%A _Wesley Ivan Hurt_, Aug 03 2019
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