A296774 Triangle read by rows in which row n lists the compositions of n ordered first by length and then reverse-lexicographically.

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, 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, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 6, 5, 1, 4, 2, 3, 3

Offset: 1

Author

Gus Wiseman, Dec 20 2017

Keywords

• nonn
• tabf

Examples

			Triangle of compositions begins:
(1),
(2),(11),
(3),(21),(12),(111),
(4),(31),(22),(13),(211),(121),(112),(1111),
(5),(41),(32),(23),(14),(311),(221),(212),(131),(122),(113),(2111),(1211),(1121),(1112),(11111).
		

Crossrefs

Cf. A066099, A101211, A108730, A124734, A228369, A281013, A294859, A296302, A296656, A296772, A296773.

Programs

Mathematica

Table[Sort[Join@@Permutations/@IntegerPartitions[n],Or[Length[#1]