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

Author

Omar E. Pol, Oct 30 2012

Keywords

• nonn
• tabf

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.

Examples

			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.