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%I #4 Dec 29 2016 05:22:26
%S 0,0,0,1,3,6,7,9,12,19,21,21,21,30,36,37,36,48,58,63,57,70,78,87,78,
%T 96,105,114,105,123,133,138,126,148,162,174,156,195,207,220,192,234,
%U 250,261,237,280,312,318,282,330,363,370,315,375,405,432,366,421,453,483,417,468,507,532,474,537,568,591,519,601,630,666,570
%N Expansion of (Sum_{k>=1} mu(k)^2*x^k)^3, where mu(k) is the Moebius function (A008683).
%C Number of ordered ways of writing n as sum of three squarefree numbers (A005117).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Squarefree.html">Squarefree</a>
%F G.f.: (Sum_{k>=1} mu(k)^2*x^k)^3.
%e a(4) = 3 because we have [2, 1, 1], [1, 2, 1] and [1, 1, 2].
%t nmax = 72; CoefficientList[Series[(Sum[MoebiusMu[k]^2 x^k, {k, 1, nmax}])^3, {x, 0, nmax}], x]
%Y Cf. A005117, A008683, A098235.
%Y Cf. A098238, A121550.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Dec 29 2016