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A057554 Lexicographic ordering of MxM, where M={0,1,2,...}.

%I A057554 #26 Oct 10 2023 16:25:22
%S A057554 0,0,0,1,1,0,0,2,1,1,2,0,0,3,1,2,2,1,3,0,0,4,1,3,2,2,3,1,4,0,0,5,1,4,
%T A057554 2,3,3,2,4,1,5,0,0,6,1,5,2,4,3,3,4,2,5,1,6,0,0,7,1,6,2,5,3,4,4,3,5,2,
%U A057554 6,1,7,0,0,8,1,7,2,6,3,5,4,4,5,3,6,2,7,1,8,0,0,9,1,8,2,7,3,6,4,5,5,4,6,3,7,2,8,1,9,0,0,10,1,9,2,8,3,7,4,6,5,5,6,4,7,3,8,2,9,1,10,0,0,11,1,10,2,9,3,8,4,7,5,6,6,5,7,4,8,3,9,2,10,1,11,0
%N A057554 Lexicographic ordering of MxM, where M={0,1,2,...}.
%C A057554 A057555 gives the lexicographic ordering of N x N, where N={1,2,3,...}.
%H A057554 Alois P. Heinz, <a href="/A057554/b057554.txt">Table of n, a(n) for n = 1..20022</a>
%e A057554 Flatten the ordered lattice points: (0,0) < (0,1) < (1,0) < (0,2) < (1,1) < ... as 0,0, 0,1, 1,0, 0,2, 1,1, ...
%t A057554 lexicographicLattice[{dim_,maxHeight_}]:= Flatten[Array[Sort@Flatten[(Permutations[#1]&)/@IntegerPartitions[#1+dim-1,{dim}],1]&,maxHeight],1]; Flatten@lexicographicLattice[{2,12}]-1 (* _Peter J. C. Moses_, Feb 10 2011 *)
%o A057554 (Python)
%o A057554 [l for i in range(20) for k in range(i,-1,-1) for l in (i-k, k)] # _Nicholas Stefan Georgescu_, Oct 10 2023
%Y A057554 Cf. A057555, A057556, A057557, A057558, A057559.
%K A057554 nonn
%O A057554 1,8
%A A057554 _Clark Kimberling_, Sep 07 2000