A296773 Triangle read by rows in which row n lists the compositions of n ordered first by decreasing length and then lexicographically.

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

Offset

1,4

Links

Table of n, a(n) for n=1..87.

Example

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

Mathematica

Table[Sort[Join@@Permutations/@IntegerPartitions[n], Or[Length[#1]>Length[#2], Length[#1]===Length[#2]&&OrderedQ[{#1, #2}]]&], {n, 6}]

Crossrefs

Cf. A066099, A101211, A108730, A124734, A228369, A281013, A294859, A296302, A296656, A296772, A296774.

Sequence in context: A275806 A362833 A228369 * A108244 A277824 A265120

Adjacent sequences: A296770 A296771 A296772 * A296774 A296775 A296776

Keyword

nonn,tabf

Author

Gus Wiseman, Dec 20 2017

Status

approved