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

Author

N. J. A. Sloane, Jan 18 2009

Keywords

• nonn
• tabf

Comments

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

Examples

			i j k
-----
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
0 1 3
0 0 4
...
		

Links

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

Crossrefs

Cf. A144627-A144629 for the individual columns.

Cf. A057556 (each triple reversed).

Programs

Maple

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: