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%I #5 Dec 20 2017 14:41:39
%S 1,1,1,2,1,1,1,1,2,2,1,3,1,1,1,1,1,1,2,1,2,1,2,1,1,1,3,2,2,3,1,4,1,1,
%T 1,1,1,1,1,1,2,1,1,2,1,1,2,1,1,2,1,1,1,1,1,3,1,2,2,1,3,1,2,1,2,2,2,1,
%U 3,1,1,1,4,2,3,3,2,4,1,5,1,1,1,1,1,1,1
%N Triangle read by rows in which row n lists the compositions of n ordered first by decreasing length and then lexicographically.
%e Triangle of compositions begins:
%e (1),
%e (11),(2),
%e (111),(12),(21),(3),
%e (1111),(112),(121),(211),(13),(22),(31),(4),
%e (11111),(1112),(1121),(1211),(2111),(113),(122),(131),(212),(221),(311),(14),(23),(32),(41),(5).
%t Table[Sort[Join@@Permutations/@IntegerPartitions[n],Or[Length[#1]>Length[#2],Length[#1]===Length[#2]&&OrderedQ[{#1,#2}]]&],{n,6}]
%Y Cf. A066099, A101211, A108730, A124734, A228369, A281013, A294859, A296302, A296656, A296772, A296774.
%K nonn,tabf
%O 1,4
%A _Gus Wiseman_, Dec 20 2017
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