A211028 A list of ordered partitions of the positive integers.

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

Offset

1,2

Comments

We start with 1. Then for each positive integer j the sequence lists the partitions of j that do not contain 1 as a part, in lexicographical order. Then the sequence lists the partitions of j-1 together with one part of size 1 as the last part of that partition. Then the partitions of j-2 together with two parts of size 1, and so on.

Links

Table of n, a(n) for n=1..89.

Example

Written as an irregular triangle, in which row n lists the partitions of n, the sequence begins:
{1};
{2},{1,1};
{3},{2,1},{1,1,1};
{2,2},{4},{3,1},{2,1,1},{1,1,1,1};
{3,2},{5},{2,2,1},{4,1},{3,1,1},{2,1,1,1},{1,1,1,1,1}};
{2,2,2},{4,2},{3,3},{6},{3,2,1},{5,1},{2,2,1,1},{4,1,1},{3,1,1,1},{2,1,1,1,1},{1,1,1,1,1,1};
...

Crossrefs

Cf. A026792, A135010.

Sequence in context: A177350 A190688 A145975 * A239001 A277648 A026792

Adjacent sequences: A211025 A211026 A211027 * A211029 A211030 A211031

Keyword

nonn,tabf

Author

Omar E. Pol, Oct 30 2012

Status

approved