A196931 Triangle read by rows in which row n lists in nondecreasing order the smallest part of every partition of n.

0, 1, 1, 2, 1, 1, 3, 1, 1, 1, 2, 4, 1, 1, 1, 1, 1, 2, 5, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Omar E. Pol, Oct 21 2011

Keywords

• nonn
• tabf

Comments

If n >= 1, row n lists the smallest parts of every partition of n in the order produced by the shell model of partitions of A135010, hence row n lists the parts of the last section of the set of partitions of n, except the emergent parts (See A182699).

Row n has length A000041(n). Row sums give A046746. Right border of triangle gives A001477. Row n starts with A000041(n-1) ones, n >= 1.

Examples

			Written as a triangle:
  0,
  1,
  1,2,
  1,1,3,
  1,1,1,2,4,
  1,1,1,1,1,2,5,
  1,1,1,1,1,1,1,2,2,3,6
  1,1,1,1,1,1,1,1,1,1,1,2,2,3,7,
  1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,8,
  ...
		

Crossrefs

Mirror of triangle A182715.

Cf. A000041, A046746, A135010, A138121, A141285, A182699, A183152, A193827, A196930.