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

0,13

Comments

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

Links

Table of n, a(n) for n=0..98.

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

Example

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
...

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:

Crossrefs

Cf. A144627-A144629 for the individual columns.

Cf. A057556 (each triple reversed).

Sequence in context: A284501 A281457 A159708 * A224772 A025442 A260118

Adjacent sequences: A144622 A144623 A144624 * A144626 A144627 A144628

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jan 18 2009

Status

approved