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%I #8 Dec 20 2017 14:41:33
%S 1,1,1,2,1,1,1,2,1,1,2,3,1,1,1,1,2,1,1,1,2,1,1,1,2,3,1,2,2,1,3,4,1,1,
%T 1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,3,1,1,2,2,1,2,1,2,1,3,1,1,2,2,
%U 1,1,3,4,1,3,2,2,3,1,4,5,1,1,1,1,1,1,2
%N Triangle read by rows in which row n lists the compositions of n ordered first by decreasing length and then reverse-lexicographically.
%C The ordering of compositions in each row is consistent with the reverse-Mathematica ordering of expressions (cf. A124734).
%C Length of k-th composition is A124748(k-1)+1. - _Andrey Zabolotskiy_, Dec 20 2017
%e Triangle of compositions begins:
%e (1),
%e (11),(2),
%e (111),(21),(12),(3),
%e (1111),(211),(121),(112),(31),(22),(13),(4),
%e (11111),(2111),(1211),(1121),(1112),(311),(221),(212),(131),(122),(113),(41),(32),(23),(14),(5).
%t Table[Reverse[Sort[Join@@Permutations/@IntegerPartitions[n]]],{n,6}]
%Y Cf. A066099, A101211, A108730, A124734, A124748, A228369, A281013, A294859, A296302, A296656, A296773, A296774.
%K nonn,tabf
%O 1,4
%A _Gus Wiseman_, Dec 20 2017
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