A183152 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, 4, 2, 3, 3, 5, 2, 4, 2, 4, 2, 3, 6, 3, 2, 2, 5, 4, 3, 5, 2, 4, 7, 3, 2, 2, 3, 6, 3, 5, 2, 4, 2, 3, 6, 3, 2, 2, 5, 4, 8, 4, 3, 2, 2, 2, 2, 4, 7, 3, 6, 5, 3, 5, 2, 4, 7, 3, 2, 2, 3, 6, 3, 5, 9, 4, 3, 3, 2, 2, 2, 2, 5, 4, 8, 4, 3, 7, 6

Offset

0,5

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 A193870. For another version see A193827. - Omar E. Pol, Aug 12 2011

Links

Table of n, a(n) for n=0..84.

Example

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

Crossrefs

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

Cf. A135010, A138121, A182707.

Sequence in context: A123725 A089080 A085058 * A210942 A368925 A368710

Adjacent sequences: A183149 A183150 A183151 * A183153 A183154 A183155

Keyword

nonn,tabf

Author

Omar E. Pol, Aug 07 2011

Status

approved