A057557 - OEIS

%I #13 Dec 04 2016 19:46:23

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

%e 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 lexicographicLattice[{dim_,maxHeight_}]:= Flatten[Array[Sort@Flatten[(Permutations[#1]&)/@IntegerPartitions[#1+dim-1,{dim}],1]&,maxHeight],1]; Flatten@lexicographicLattice[{3,6}]

%t (* By _Peter J. C. Moses_, Feb 10 2011 *)

%Y A057555: ordering of N^2

%Y A057559: ordering of N^4

%Y A186006: ordering of N^5

%Y A186003: distances to the plane x=0

%Y A186004: distances to the plane y=0

%Y A186005: distances to the plane z=0

%K nonn

%O 1,6

%A _Clark Kimberling_, Sep 07 2000

%E Corrected and extended by _Clark Kimberling_,, Feb 10 2011.