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

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, 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, 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

Offset

1,8

Comments

A057555 gives the lexicographic ordering of N x N, where N={1,2,3,...}.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20022

Example

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, ...

Mathematica

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 *)

Prog

(Python)
[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

Crossrefs

Cf. A057555, A057556, A057557, A057558, A057559.

Sequence in context: A132401 A104273 A051778 * A060575 A236074 A099916

Adjacent sequences: A057551 A057552 A057553 * A057555 A057556 A057557

Keyword

nonn

Author

Clark Kimberling, Sep 07 2000

Status

approved