

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.


7



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
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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:
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.
Sequence in context: A023581 A023574 A210941 * A131340 A175470 A098534
Adjacent sequences: A193824 A193825 A193826 * A193828 A193829 A193830


KEYWORD

nonn,tabf


AUTHOR

Omar E. Pol, Aug 12 2011


STATUS

approved



