A339351 Irregular triangle read by rows in which row n lists the compositions (ordered partitions) of n into distinct parts in lexicographic order.

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

Offset

1,2

Links

Table of n, a(n) for n=1..128.

Index entries for sequences related to compositions

Example

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

Mathematica

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

Crossrefs

Cf. A026793, A066099, A097910 (row lengths), A118457, A228369, A246688, A304797 (row sums), A339178.

Sequence in context: A329173 A366493 A352998 * A284322 A219607 A205451

Adjacent sequences: A339348 A339349 A339350 * A339352 A339353 A339354

Keyword

nonn,tabf

Author

Ilya Gutkovskiy, Dec 01 2020

Status

approved