login
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.
7

%I #7 Aug 17 2023 11:06:09

%S 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,

%T 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,

%U 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

%N 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.

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

%H N. J. A. Sloane, <a href="/A144625/a144625.txt">The 6545 triples with i+j+k <= 32</a>

%e i j k

%e -----

%e 0 0 0

%e 1 0 0

%e 0 1 0

%e 0 0 1

%e 2 0 0

%e 1 1 0

%e 0 2 0

%e 1 0 1

%e 0 1 1

%e 0 0 2

%e 3 0 0

%e 2 1 0

%e 1 2 0

%e 0 3 0

%e 2 0 1

%e 1 1 1

%e 0 2 1

%e 1 0 2

%e 0 1 2

%e 0 0 3

%e 4 0 0

%e 3 1 0

%e 2 2 0

%e 1 3 0

%e 0 4 0

%e 3 0 1

%e 2 1 1

%e 1 2 1

%e 0 3 1

%e 2 0 2

%e 1 1 2

%e 0 2 2

%e 1 0 3

%e 0 1 3

%e 0 0 4

%e ...

%p for n from 0 to 7 do

%p for k from 0 to n do

%p for j from 0 to n do

%p for i from 0 to n do

%p if i+j+k=n then lprint(i,j,k); fi;

%p od: od: od: od:

%Y Cf. A144627-A144629 for the individual columns.

%Y Cf. A057556 (each triple reversed).

%K nonn,tabf

%O 0,13

%A _N. J. A. Sloane_, Jan 18 2009