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

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

1,2

Links

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

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.

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

Prog

(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

Crossrefs

Cf. A001399 (runlengths of sums), A098294.

Sequence in context: A200596 A088422 A100833 * A296656 A303945 A026793

Adjacent sequences: A097290 A097291 A097292 * A097294 A097295 A097296

Keyword

nonn,look

Author

Clark Kimberling, Aug 05 2004

Status

approved