A337259 Compositions, sorted by increasing sum, increasing length and decreasing colexicographical order.

1, 2, 1, 1, 3, 1, 2, 2, 1, 1, 1, 1, 4, 1, 3, 2, 2, 3, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 5, 1, 4, 2, 3, 3, 2, 4, 1, 1, 1, 3, 1, 2, 2, 2, 1, 2, 1, 3, 1, 2, 2, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 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), (1, 2), (2, 1), (1, 1, 1),
(4), (1, 3), (2, 2), (3, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 1, 1),
(5), (1, 4), (2, 3), (3, 2), (4, 1), (1, 1, 3), (1, 2, 2), (2, 1, 2), (1, 3, 1), (2, 2, 1), (3, 1, 1), (1, 1, 1, 2), (1, 1, 2, 1), (1, 2, 1, 1), (2, 1, 1, 1), (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(ListTools:-Reverse([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. A337243 (increasing length, then 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: A115758 A228351 A124734 * A037034 A340056 A229897

Adjacent sequences: A337256 A337257 A337258 * A337260 A337261 A337262

Keyword

nonn,tabf

Author

Lorenzo Sauras Altuzarra, Aug 21 2020

Status

approved