A337260 Compositions, sorted by increasing sum, decreasing length and increasing colexicographical order.

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

Offset

1,4

Links

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

Example

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

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, i-j+1))]:
      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. A337259 (increasing length, then reverse colexicographic).

Cf. A296773 (decreasing length, then lexicographic).

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

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

Cf. A228369 (lexicographic).

Cf. A066099 (reverse lexicographic).

Cf. A228525 (colexicographic).

Cf. A228351 (reverse colexicographic).

Sequence in context: A097847 A275120 A144379 * A296772 A228525 A352823

Adjacent sequences: A337257 A337258 A337259 * A337261 A337262 A337263

Keyword

nonn,tabf

Author

Lorenzo Sauras Altuzarra, Aug 21 2020

Status

approved