A057556 -id:A057556 - cp's OEIS frontend

A144625 List of triples (i,j,k) (i>=0, j>=0, k>=0) in canonical order used to convert an infinite tetrahedron of numbers to a linear sequence.

0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 2, 0, 1, 0, 1, 0, 1, 1, 0, 0, 2, 3, 0, 0, 2, 1, 0, 1, 2, 0, 0, 3, 0, 2, 0, 1, 1, 1, 1, 0, 2, 1, 1, 0, 2, 0, 1, 2, 0, 0, 3, 4, 0, 0, 3, 1, 0, 2, 2, 0, 1, 3, 0, 0, 4, 0, 3, 0, 1, 2, 1, 1, 1, 2, 1, 0, 3, 1, 2, 0, 2, 1, 1, 2, 0, 2, 2, 1, 0, 3

Offset: 0

N. J. A. Sloane, Jan 18 2009

The triples are sorted first according to their sum, then by the value of k, then by the value of j.

N. J. A. Sloane, The 6545 triples with i+j+k <= 32

Cf. A144627-A144629 for the individual columns.

Cf. A057556 (each triple reversed).

for n from 0 to 7 do
for k from 0 to n do
for j from 0 to n do
for i from 0 to n do
if i+j+k=n then lprint(i,j,k); fi;
od: od: od: od:

A057559 Lexicographic ordering of NxNxNxN, where N={1,2,3,...}.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 3, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 3, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 3, 1, 1, 3, 2, 1, 1, 4, 1, 1, 2, 1, 3, 1, 2, 2, 2, 1, 2, 3, 1, 1, 3, 1, 2, 1, 3, 2, 1, 1, 4, 1, 1, 2, 1, 1, 3, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 3, 1, 1, 3, 1, 1, 2, 3, 1, 2, 1, 3, 2, 1, 1, 4, 1, 1, 1

Offset: 1

Clark Kimberling, Sep 07 2000

nonn

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

Cf. A057554, A057555, A057556, A057557, A057558, A186006.

lexicographicLattice[{dim_,maxHeight_}]:= Flatten[Array[Sort@Flatten[(Permutations[#1]&)/@IntegerPartitions[#1+dim-1,{dim}],1]&,maxHeight],1]; Flatten@lexicographicLattice[{4,4}]
(* by Peter J. C. Moses, Feb 10 2011 *)

Extended by Clark Kimberling, Feb 10 2011

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

Original entry on oeis.org

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

Clark Kimberling, Sep 07 2000

nonn

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

			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, ...

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

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

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 *)

[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

A057558 Lexicographic ordering of MxMxMxM, where M={0,1,2,...}.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 2, 0, 0, 2, 1, 0, 0, 3, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 1, 2, 0, 0, 2, 0, 1, 0, 2, 1, 0, 0, 3, 0, 0, 1, 0, 0, 2, 1, 0, 1, 1, 1, 0, 2, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 2, 0, 0, 2, 0, 0, 1, 2, 0, 1, 0, 2, 1, 0, 0, 3, 0, 0, 0

Offset: 1

Clark Kimberling, Sep 07 2000

nonn

			Flatten the list of ordered lattice points, (0,0,0,0) < (0,0,0,1) < (0,0,1,0) < ... as 0,0,0,0, 0,0,0,1, 0,0,1,0, ...

Alois P. Heinz, Table of n, a(n) for n = 1..19380

Cf. A057556, A057557, A057559.

lexicographicLattice[{dim_,maxHeight_}]:= Flatten[Array[Sort@Flatten[(Permutations[#1]&)/@IntegerPartitions[#1+dim-1,{dim}],1]&,maxHeight],1]; Flatten@lexicographicLattice[{4,4}]-1
(* by Peter J. C. Moses, Feb 10 2011 *)

Extended by Clark Kimberling, Feb 10 2011

cp's OEIS Frontend

A144625 List of triples (i,j,k) (i>=0, j>=0, k>=0) in canonical order used to convert an infinite tetrahedron of numbers to a linear sequence.

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A057559 Lexicographic ordering of NxNxNxN, where N={1,2,3,...}.

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

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A057558 Lexicographic ordering of MxMxMxM, where M={0,1,2,...}.

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Mathematica

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