A193827 Irregular triangle read by rows in which row n lists the emergent parts of all partitions of n, or 0 if such parts do not exist.

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

Offset: 0

Author

Omar E. Pol, Aug 12 2011

Keywords

• nonn
• tabf

Comments

For the definition of "emergent part" see A182699 and also A182709. Also [0, 0, 0, 0] followed by the positive integers of the rows that contain zeros in the triangle A186114. For another version see A183152.

Examples

			If written as a triangle:
0,
0,
0,
0,
2,
3,
2,2,4,3,
3,2,5,4,
2,2,4,3,2,2,3,6,5,4,
3,2,5,4,2,2,3,7,3,3,6,5,
2,2,4,3,2,2,3,6,5,4,2,2,2,2,3,4,8,4,3,7,6,5,
3,2,5,4,2,2,3,7,3,3,6,5,2,2,2,2,3,3,4,9,5,4,3,4,8,7,6
		

Crossrefs

Row n has length A182699(n). Row sums give A182709.

Cf. A135010, A138121.