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%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
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