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A057558 Lexicographic ordering of MxMxMxM, where M={0,1,2,...}.

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%I A057558 #13 Aug 16 2023 19:37:51
%S A057558 0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,0,0,0,0,0,2,0,0,1,1,0,0,2,0,0,1,
%T A057558 0,1,0,1,1,0,0,2,0,0,1,0,0,1,1,0,1,0,1,1,0,0,2,0,0,0,0,0,0,3,0,0,1,2,
%U A057558 0,0,2,1,0,0,3,0,0,1,0,2,0,1,1,1,0,1,2,0,0,2,0,1,0,2,1,0,0,3,0,0,1,0,0,2,1,0,1,1,1,0,2,0,1,1,0,1,1,1,1,0,1,2,0,0,2,0,0,1,2,0,1,0,2,1,0,0,3,0,0,0
%N A057558 Lexicographic ordering of MxMxMxM, where M={0,1,2,...}.
%H A057558 Alois P. Heinz, <a href="/A057558/b057558.txt">Table of n, a(n) for n = 1..19380</a>
%e A057558 Flatten the list of ordered lattice points, (0,0,0,0) < (0,0,0,1) < (0,0,1,0) < ... as 0,0,0,0, 0,0,0,1, 0,0,1,0, ...
%t A057558 lexicographicLattice[{dim_,maxHeight_}]:= Flatten[Array[Sort@Flatten[(Permutations[#1]&)/@IntegerPartitions[#1+dim-1,{dim}],1]&,maxHeight],1]; Flatten@lexicographicLattice[{4,4}]-1
%t A057558 (* by _Peter J. C. Moses_, Feb 10 2011 *)
%Y A057558 Cf. A057556, A057557, A057559.
%K A057558 nonn
%O A057558 1,24
%A A057558 _Clark Kimberling_, Sep 07 2000
%E A057558 Extended by _Clark Kimberling_, Feb 10 2011