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A057556 Lexicographic ordering of M x M x M, where M={0,1,2,...}.

%I A057556 #23 Aug 17 2023 11:06:03
%S A057556 0,0,0,0,0,1,0,1,0,1,0,0,0,0,2,0,1,1,0,2,0,1,0,1,1,1,0,2,0,0,0,0,3,0,
%T A057556 1,2,0,2,1,0,3,0,1,0,2,1,1,1,1,2,0,2,0,1,2,1,0,3,0,0,0,0,4,0,1,3,0,2,
%U A057556 2,0,3,1,0,4,0,1,0,3,1,1,2,1,2,1,1,3,0,2,0,2,2,1,1,2,2,0,3,0,1,3,1,0,4,0,0,0,0,5,0,1,4,0,2,3,0,3,2,0,4,1,0,5,0,1,0,4,1,1,3,1,2,2,1,3,1,1,4,0,2,0,3,2,1,2,2,2,1,2,3,0,3,0,2,3,1,1,3,2,0,4,0,1,4,1,0,5,0,0
%N A057556 Lexicographic ordering of M x M x M, where M={0,1,2,...}.
%C A057556 See A057557 for N x N x N, where N={1,2,3,...}.
%C A057556 The triples are sorted first according to their sum, then lexicographically. - _Pontus von Brömssen_, Aug 16 2023
%H A057556 Alois P. Heinz, <a href="/A057556/b057556.txt">Table of n, a(n) for n = 1..10962</a>
%e A057556 Flatten the list of ordered lattice points, (0,0,0) < (0,0,1) < (0,1,0) < ... to 0,0,0, 0,0,1, 0,1,0, ...
%e A057556 As a three-column array:
%e A057556   0 0 0
%e A057556   0 0 1
%e A057556   0 1 0
%e A057556   1 0 0
%e A057556   0 0 2
%e A057556   0 1 1
%e A057556   0 2 0
%e A057556   1 0 1
%e A057556   1 1 0
%e A057556   2 0 0
%e A057556   0 0 3
%e A057556   0 1 2
%e A057556   0 2 1
%e A057556   0 3 0
%e A057556   1 0 2
%e A057556   1 1 1
%e A057556   1 2 0
%e A057556   2 0 1
%e A057556   2 1 0
%e A057556   3 0 0
%e A057556   ...
%t A057556 lexicographicLattice[{dim_,maxHeight_}]:= Flatten[Array[Sort@Flatten[(Permutations[#1]&)/@IntegerPartitions[#1+dim-1,{dim}],1]&,maxHeight],1]; Flatten@lexicographicLattice[{3,6}]-1
%t A057556 (* _Peter J. C. Moses_, Feb 10 2011 *)
%Y A057556 Cf. A057554, A057557.
%Y A057556 Cf. A144625 (each triple reversed).
%K A057556 nonn,tabf
%O A057556 1,15
%A A057556 _Clark Kimberling_, Sep 07 2000
%E A057556 Extended by _Clark Kimberling_, Feb 10 2011