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

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, 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, 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

Offset: 1

Author

Clark Kimberling, Sep 07 2000

Keywords

• nonn
• tabf

Comments

See A057557 for N x N x N, where N={1,2,3,...}.

The triples are sorted first according to their sum, then lexicographically. - Pontus von Brömssen, Aug 16 2023

Examples

			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, ...
As a three-column array:
  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 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
  ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10962

Crossrefs

Cf. A057554, A057557.

Cf. A144625 (each triple reversed).

Programs

Mathematica

lexicographicLattice[{dim_,maxHeight_}]:= Flatten[Array[Sort@Flatten[(Permutations[#1]&)/@IntegerPartitions[#1+dim-1,{dim}],1]&,maxHeight],1]; Flatten@lexicographicLattice[{3,6}]-1
(* Peter J. C. Moses, Feb 10 2011 *)

Extensions

Extended by Clark Kimberling, Feb 10 2011