A337243 Compositions, sorted by increasing sum, increasing length, and increasing colexicographical order.

1, 2, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 3, 1, 2, 2, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 5, 4, 1, 3, 2, 2, 3, 1, 4, 3, 1, 1, 2, 2, 1, 1, 3, 1, 2, 1, 2, 1, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1

Offset: 1

Author

Lorenzo Sauras Altuzarra, Aug 21 2020

Keywords

• nonn
• tabf

Examples

			The first 5 rows are:
(1),
(2), (1, 1),
(3), (2, 1), (1, 2), (1, 1, 1),
(4), (3, 1), (2, 2), (1, 3), (2, 1, 1), (1, 2, 1), (1, 1, 2), (1, 1, 1, 1),
(5), (4, 1), (3, 2), (2, 3), (1, 4), (3, 1, 1), (2, 2, 1), (1, 3, 1), (2, 1, 2), (1, 2, 2), (1, 1, 3), (2, 1, 1, 1), (1, 2, 1, 1), (1, 1, 2, 1), (1, 1, 1, 2), (1, 1, 1, 1, 1).
		

Crossrefs

Cf. A124734 (increasing length, then lexicographic).

Cf. A296774 (increasing length, then reverse lexicographic).

Cf. A337259 (increasing length, then reverse colexicographic).

Cf. A296773 (decreasing length, then lexicographic).

Cf. A296772 (decreasing length, then reverse lexicographic).

Cf. A337260 (decreasing length, then colexicographic).

Cf. A108244 (decreasing length, then reverse colexicographic).

Cf. A228369 (lexicographic).

Cf. A066099 (reverse lexicographic).

Cf. A228525 (colexicographic).

Cf. A228351 (reverse colexicographic).

Programs

Maple

List := proc(n)
   local i, j, k, L:
   L := []:
   for i from 1 to n do
      for j from 1 to i do
         L := [op(L), op(combinat:-composition(i, j))]:
      od:
   od:
   for k from 1 to numelems(L) do L[k] := ListTools:-Reverse(L[k]): od:
   L:
end: