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A057557 Lexicographic ordering of NxNxN, where N={1,2,3,...}.

%I A057557 #13 Dec 04 2016 19:46:23
%S A057557 1,1,1,1,1,2,1,2,1,2,1,1,1,1,3,1,2,2,1,3,1,2,1,2,2,2,1,3,1,1,1,1,4,1,
%T A057557 2,3,1,3,2,1,4,1,2,1,3,2,2,2,2,3,1,3,1,2,3,2,1,4,1,1,1,1,5,1,2,4,1,3,
%U A057557 3,1,4,2,1,5,1,2,1,4,2,2,3,2,3,2,2,4,1,3,1,3,3,2,2,3,3,1,4,1,2,4,2,1,5,1,1,1,1,6,1,2,5,1,3,4,1,4,3,1,5,2,1,6,1,2,1,5,2,2,4,2,3,3,2,4,2,2,5,1,3,1,4,3,2,3,3,3,2,3,4,1,4,1,3,4,2,2,4,3,1,5,1,2,5,2,1,6,1,1
%N A057557 Lexicographic ordering of NxNxN, where N={1,2,3,...}.
%e A057557 Flatten the list of ordered lattice points, (1,1,1) < (1,1,2) < (1,2,1) < ..., to 1,1,1, 1,1,2, 1,2,1, ...
%t A057557 lexicographicLattice[{dim_,maxHeight_}]:= Flatten[Array[Sort@Flatten[(Permutations[#1]&)/@IntegerPartitions[#1+dim-1,{dim}],1]&,maxHeight],1]; Flatten@lexicographicLattice[{3,6}]
%t A057557 (* By _Peter J. C. Moses_, Feb 10 2011 *)
%Y A057557 A057555: ordering of N^2
%Y A057557 A057559: ordering of N^4
%Y A057557 A186006: ordering of N^5
%Y A057557 A186003: distances to the plane x=0
%Y A057557 A186004: distances to the plane y=0
%Y A057557 A186005: distances to the plane z=0
%K A057557 nonn
%O A057557 1,6
%A A057557 _Clark Kimberling_, Sep 07 2000
%E A057557 Corrected and extended by _Clark Kimberling_,, Feb 10 2011.