A337243 - OEIS

%I #41 Sep 28 2020 21:38:15

%S 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,

%T 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,

%U 1,2,1,1,1,1,2,1,1,1,1,1

%N Compositions, sorted by increasing sum, increasing length, and increasing colexicographical order.

%e The first 5 rows are:

%e (1),

%e (2), (1, 1),

%e (3), (2, 1), (1, 2), (1, 1, 1),

%e (4), (3, 1), (2, 2), (1, 3), (2, 1, 1), (1, 2, 1), (1, 1, 2), (1, 1, 1, 1),

%e (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).

%p List := proc(n)

%p    local i, j, k, L:

%p    L := []:

%p    for i from 1 to n do

%p       for j from 1 to i do

%p          L := [op(L), op(combinat:-composition(i, j))]:

%p       od:

%p    od:

%p    for k from 1 to numelems(L) do L[k] := ListTools:-Reverse(L[k]): od:

%p    L:

%p end:

%Y Cf. A124734 (increasing length, then lexicographic).

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

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

%Y Cf. A296773 (decreasing length, then lexicographic).

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

%Y Cf. A337260 (decreasing length, then colexicographic).

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

%Y Cf. A228369 (lexicographic).

%Y Cf. A066099 (reverse lexicographic).

%Y Cf. A228525 (colexicographic).

%Y Cf. A228351 (reverse colexicographic).

%K nonn,tabf

%O 1,2

%A _Lorenzo Sauras Altuzarra_, Aug 21 2020