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

1,2

Links

Table of n, a(n) for n=1..80.

Example

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).

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:

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).

Sequence in context: A171850 A356144 A087782 * A296774 A066099 A254111

Adjacent sequences: A337240 A337241 A337242 * A337244 A337245 A337246

Keyword

nonn,tabf

Author

Lorenzo Sauras Altuzarra, Aug 21 2020

Status

approved