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%I #15 Oct 10 2019 14:02:47
%S 2,2,2,3,5,6,8,15,29,48,71,112,216,445,849,1459,2403,4239,8343,17049,
%T 33416,61192,107290,190803,361136,722568,1457638,2847209,5322619,
%U 9679593,17715193,33626815,66430582,133432610,264832126,511136916,960634698,1786150886
%N Number of subsets of {1,2,3,...,n} whose sum is a cube.
%H Alois P. Heinz, <a href="/A126111/b126111.txt">Table of n, a(n) for n = 1..300</a>
%e There are five subsets of {1,2,3,4,5} that sum to a cube: {}, {1},{3,5}, {1,2,5} and {1,3,4}. Thus a(5)=5.
%t g[n_] := Block[{p = Product[1 + z^i, {i, n}]},Sum[Boole[IntegerQ[k^(1/3)]]*Coefficient[p, z, k], {k, 0, n*(n + 1)/2}]];Array[g, 37] (* _Ray Chandler_, Mar 07 2007 *)
%Y Cf. number of subsets of {1,2,3,...,n} whose sum is a square/prime in A126024, A127542.
%K nonn
%O 1,1
%A _Zak Seidov_, Mar 05 2007
%E Extended by _Ray Chandler_, Mar 07 2007
%E More terms from _Alois P. Heinz_, Jan 18 2014