A182715 Triangle read by rows in which row n lists in nonincreasing order the smallest part of every partition of n.

0, 1, 2, 1, 3, 1, 1, 4, 2, 1, 1, 1, 5, 2, 1, 1, 1, 1, 1, 6, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 7, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 4, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Omar E. Pol, Dec 01 2010

Keywords

• nonn
• tabf

Comments

Triangle read by rows in which row n lists the smallest parts of all partitions of n in the order produced by the shell model of partitions of A138121.

Also, row n lists the "filler parts" of all partition of n. For more information see A182699.

Row n has length A000041(n). Row sums give A046746. Column 1 gives A001477. The last A000041(n-1) terms of row n are ones, n >= 1.

Examples

			For row 10, see the illustration of the link.
Triangle begins:
  0,
  1,
  2,1,
  3,1,1,
  4,2,1,1,1,
  5,2,1,1,1,1,1,
  6,3,2,2,1,1,1,1,1,1,1,
  7,3,2,2,1,1,1,1,1,1,1,1,1,1,1,
  8,4,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
  9,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
  ...
		

Links

• Omar E. Pol, Illustration of the smallest parts of all partitions of 10 (colored blue) in the shell model of partitions

Crossrefs

Cf. A026807, A135010, A138121, A141285, A182699, A182709.

Mirror of triangle A196931.

Extensions

Name simplified and more terms from Omar E. Pol, Oct 21 2011