A193827 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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 A186114. For another version see A183152.

LINKS

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

EXAMPLE

If written as a triangle:

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.