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%I #12 May 09 2024 11:56:37
%S 1,2,3,1,2,4,1,2,5,1,3,4,1,2,6,1,3,5,2,3,4,1,2,7,1,3,6,1,4,5,2,3,5,1,
%T 2,8,1,3,7,1,4,6,2,3,6,2,4,5,1,2,9,1,3,8,1,4,7,1,5,6,2,3,7,2,4,6,3,4,
%U 5,1,2,10,1,3,9,1,4,8,1,5,7,2,3,8,2,4,7,2,5,6,3,4,6,1,2,11,1,3,10,1,4,9,1,5,8
%N Contains exactly once every triple i,j,k such that 0<i<j<k.
%H Robert Israel, <a href="/A097293/b097293.txt">Table of n, a(n) for n = 1..10092</a> (triples with sum <= 52)
%F Terms are lexically ordered in triples by sum: 1 2 3 (sum = 6) 1 2 4 (sum = 7) 1 2 5, then 1 3 4 (two triples having sum = 8), etc.
%p f:= proc(n) local i,j;
%p seq(seq(op([i,j,n-i-j]),j = i+1 .. (n-i-1)/2),i=1..n/3);
%p end proc:
%p map(f, [$1..20]); # _Robert Israel_, May 09 2024
%o (PARI) a_rows(N) = [[Vec(e)+[0,1,2] |e<-partitions(n,,[3,3])] |n<-[3..N+2]]; \\ _Ruud H.G. van Tol_, May 09 2024
%Y Cf. A001399 (runlengths of sums), A098294.
%K nonn,look
%O 1,2
%A _Clark Kimberling_, Aug 05 2004