A339178 Irregular triangle read by rows in which row n lists the compositions (ordered partitions) of n into distinct parts in reverse lexicographic order.

1, 2, 3, 2, 1, 1, 2, 4, 3, 1, 1, 3, 5, 4, 1, 3, 2, 2, 3, 1, 4, 6, 5, 1, 4, 2, 3, 2, 1, 3, 1, 2, 2, 4, 2, 3, 1, 2, 1, 3, 1, 5, 1, 3, 2, 1, 2, 3, 7, 6, 1, 5, 2, 4, 3, 4, 2, 1, 4, 1, 2, 3, 4, 2, 5, 2, 4, 1, 2, 1, 4, 1, 6, 1, 4, 2, 1, 2, 4, 8, 7, 1, 6, 2, 5, 3, 5, 2, 1, 5, 1, 2, 4, 3, 1, 4, 1, 3, 3, 5, 3, 4, 1, 3, 1, 4, 2, 6, 2, 5, 1, 2, 1, 5, 1, 7, 1, 5, 2, 1, 4, 3, 1, 3, 4, 1, 2, 5

Offset: 1

Author

Ilya Gutkovskiy, Nov 26 2020

Keywords

• nonn
• tabf

Examples

			Triangle begins:
[1],
[2],
[3], [2, 1], [1, 2],
[4], [3, 1], [1, 3],
[5], [4, 1], [3, 2], [2, 3], [1, 4],
...
		

Links

• Index entries for sequences related to compositions

Crossrefs

Cf. A026793, A066099, A097910 (row lengths), A118457, A228369, A246688, A304797 (row sums).

Programs

Mathematica

Table[Sort[Join @@ Permutations /@ Select[IntegerPartitions[n], UnsameQ @@ # &], OrderedQ[PadRight[{#2, #1}]] &], {n, 8}] // Flatten