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%I #16 Aug 04 2018 06:38:21
%S 0,4,32,272,256,1156,2176,3692,2048,8496,9248,15196,17408,22324,29536,
%T 39820,16384,56144,67968,79252,73984,111956,121568,143176,139264,
%U 184852,178592,238884,236288,285940,318560,358004,131072,435396,449152
%N Volume (multiplied by 3) of polyhedron formed by points (i,j,k) in Z^3 with i^2+j^2+k^2 = n^2.
%C For n=2^k, a(n)=4 n^3 because A016727(2^k) = SumOfSquaresRepresentations[3,(2^k)^2] contains only {0,0,2^k}.
%C This is why a(16) and a(32) are visibly so much smaller than their neighbors when you look at the graph. [_Jonathan Vos Post_, Apr 22 2011]
%e a(2) = 32 because the volume of the polyhedron formed by all integer points at distance 2 from the origin, {{-2, 0, 0}, {0, -2, 0}, {0, 0, -2}, {0, 0, 2}, {0, 2, 0}, {2, 0, 0}}, is 32/3.
%t forms[ z:{_Integer, _, _} ] := Union[ Flatten[ Permutations/@(Times[ z, # ]&/@Flatten[ Outer[ List, {1, -1}, {1, -1}, {1, -1} ], 2 ]), 1 ] ]; polyhedra=Flatten[ forms/@SumOfSquaresRepresentations[ 3, # ], 1 ]&/@(Range[ 1, 36 ]^2); HullVolume[ #, ConvexHull3D[ # ] ]&/@polyhedra;
%Y Cf. A016727.
%K nonn
%O 0,2
%A _Wouter Meeussen_, Nov 10 2001
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