A296773 - OEIS

%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