A186006 Lexicographic ordering of N x N x N x N x N, where N={1,2,3,...}.

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

Offset

1,10

Comments

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.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Example

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, ...

Mathematica

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]
(* Peter J. C. Moses, Feb 10 2011 *)

Crossrefs

Cf. A057555, A057557, A057559.

Sequence in context: A378322 A088951 A361633 * A236398 A107453 A164115

Adjacent sequences: A186003 A186004 A186005 * A186007 A186008 A186009

Keyword

nonn

Author

Clark Kimberling, Feb 10 2011

Status

approved