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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.

%I A144625 #7 Aug 17 2023 11:06:09
%S A144625 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 A144625 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 A144625 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 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.
%C A144625 The triples are sorted first according to their sum, then by the value of k, then by the value of j.
%H A144625 N. J. A. Sloane, <a href="/A144625/a144625.txt">The 6545 triples with i+j+k <= 32</a>
%e A144625 i j k
%e A144625 -----
%e A144625 0 0 0
%e A144625 1 0 0
%e A144625 0 1 0
%e A144625 0 0 1
%e A144625 2 0 0
%e A144625 1 1 0
%e A144625 0 2 0
%e A144625 1 0 1
%e A144625 0 1 1
%e A144625 0 0 2
%e A144625 3 0 0
%e A144625 2 1 0
%e A144625 1 2 0
%e A144625 0 3 0
%e A144625 2 0 1
%e A144625 1 1 1
%e A144625 0 2 1
%e A144625 1 0 2
%e A144625 0 1 2
%e A144625 0 0 3
%e A144625 4 0 0
%e A144625 3 1 0
%e A144625 2 2 0
%e A144625 1 3 0
%e A144625 0 4 0
%e A144625 3 0 1
%e A144625 2 1 1
%e A144625 1 2 1
%e A144625 0 3 1
%e A144625 2 0 2
%e A144625 1 1 2
%e A144625 0 2 2
%e A144625 1 0 3
%e A144625 0 1 3
%e A144625 0 0 4
%e A144625 ...
%p A144625 for n from 0 to 7 do
%p A144625 for k from 0 to n do
%p A144625 for j from 0 to n do
%p A144625 for i from 0 to n do
%p A144625 if i+j+k=n then lprint(i,j,k); fi;
%p A144625 od: od: od: od:
%Y A144625 Cf. A144627-A144629 for the individual columns.
%Y A144625 Cf. A057556 (each triple reversed).
%K A144625 nonn,tabf
%O A144625 0,13
%A A144625 _N. J. A. Sloane_, Jan 18 2009