A057557 Lexicographic ordering of NxNxN, where N={1,2,3,...}.

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 3, 1, 2, 2, 1, 3, 1, 2, 1, 2, 2, 2, 1, 3, 1, 1, 1, 1, 4, 1, 2, 3, 1, 3, 2, 1, 4, 1, 2, 1, 3, 2, 2, 2, 2, 3, 1, 3, 1, 2, 3, 2, 1, 4, 1, 1, 1, 1, 5, 1, 2, 4, 1, 3, 3, 1, 4, 2, 1, 5, 1, 2, 1, 4, 2, 2, 3, 2, 3, 2, 2, 4, 1, 3, 1, 3, 3, 2, 2, 3, 3, 1, 4, 1, 2, 4, 2, 1, 5, 1, 1, 1, 1, 6, 1, 2, 5, 1, 3, 4, 1, 4, 3, 1, 5, 2, 1, 6, 1, 2, 1, 5, 2, 2, 4, 2, 3, 3, 2, 4, 2, 2, 5, 1, 3, 1, 4, 3, 2, 3, 3, 3, 2, 3, 4, 1, 4, 1, 3, 4, 2, 2, 4, 3, 1, 5, 1, 2, 5, 2, 1, 6, 1, 1

Offset

1,6

Links

Table of n, a(n) for n=1..168.

Example

Flatten the list of ordered lattice points, (1,1,1) < (1,1,2) < (1,2,1) < ..., to 1,1,1, 1,1,2, 1,2,1, ...

Mathematica

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

Crossrefs

A057555: ordering of N^2

A057559: ordering of N^4

A186006: ordering of N^5

A186003: distances to the plane x=0

A186004: distances to the plane y=0

A186005: distances to the plane z=0

Sequence in context: A330098 A189024 A304720 * A353364 A328390 A325599

Adjacent sequences: A057554 A057555 A057556 * A057558 A057559 A057560

Keyword

nonn

Author

Clark Kimberling, Sep 07 2000

Extensions

Corrected and extended by Clark Kimberling,, Feb 10 2011.

Status

approved