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%I #4 Dec 20 2017 14:41:47
%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 1,3,2,2,3,1,4,3,1,1,2,2,1,2,1,2,1,3,1,1,2,2,1,1,3,2,1,1,1,1,2,1,1,1,
%U 1,2,1,1,1,1,2,1,1,1,1,1,6,5,1,4,2,3,3
%N Triangle read by rows in which row n lists the compositions of n ordered first by length and then reverse-lexicographically.
%e Triangle of compositions begins:
%e (1),
%e (2),(11),
%e (3),(21),(12),(111),
%e (4),(31),(22),(13),(211),(121),(112),(1111),
%e (5),(41),(32),(23),(14),(311),(221),(212),(131),(122),(113),(2111),(1211),(1121),(1112),(11111).
%t Table[Sort[Join@@Permutations/@IntegerPartitions[n],Or[Length[#1]<Length[#2],Length[#1]===Length[#2]&&OrderedQ[{#2,#1}]]&],{n,6}]
%Y Cf. A066099, A101211, A108730, A124734, A228369, A281013, A294859, A296302, A296656, A296772, A296773.
%K nonn,tabf
%O 1,2
%A _Gus Wiseman_, Dec 20 2017