A097293 Contains exactly once every triple i,j,k such that 0

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, 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, 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

Offset: 1

Author

Clark Kimberling, Aug 05 2004

Keywords

• nonn
• look

Links

• Robert Israel, Table of n, a(n) for n = 1..10092 (triples with sum <= 52)

Crossrefs

Cf. A001399 (runlengths of sums), A098294.

Programs

Maple

f:= proc(n) local i,j;
  seq(seq(op([i,j,n-i-j]),j = i+1 .. (n-i-1)/2),i=1..n/3);
end proc:
map(f, [$1..20]); # Robert Israel, May 09 2024

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

Formula

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.