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A186006
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Lexicographic ordering of N x N x N x N x N, where N={1,2,3,...}.
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3
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1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 2, 3, 1, 1, 1, 3, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 3, 1, 1, 2, 2, 2, 1, 1, 2, 3, 1, 1, 1, 3, 1, 2, 1, 1, 3, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 3
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OFFSET
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1,10
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COMMENTS
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By changing a single number, the Mathematica code suffices for other dimensions: N x N (A057555), N x N x N (A057557), N x N x N x N (A057559), and higher.
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LINKS
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EXAMPLE
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First, list the 5-tuples in lexicographic order: (1,1,1,1,1) < (1,1,1,1,2) < (1,1,1,2,1) < (1,1,2,1,1) < ... < (1,2,2,1,1) < (1,1,3,1,1) < ... Then flatten the list, leaving 1,1,1,1,1, 1,1,1,1,2, 1,1,1,2,1, 1,1,2,1,1, ...
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MATHEMATICA
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lexicographicLattice[{dim_, maxHeight_}]:= Flatten[Array[Sort@Flatten[(Permutations[#1]&)/@IntegerPartitions[#1+dim-1, {dim}], 1]&, maxHeight], 1];
lexicographicLatticeHeightArray[{dim_, maxHeight_, axis_}]:= Array[Flatten@Position[Map[#[[axis]]&, lexicographicLattice[{dim, maxHeight}]], #]&, maxHeight]
Take[Flatten@lexicographicLattice[{5, 12}], 160]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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