

A115965


Number of planar subpartitions of size n pyramidal planar partition.


0




OFFSET

0,2


COMMENTS

This is a 2dimensional analog of the Catalan numbers C_n (A000108). The number of subpartitions of the triangular partition [n,n1,...,1] is C_{n+1}. The planar partition having its subpartitions counted is:
n n1 ... 2 1
n1 n2 ... 1
... ...
2 1
1


LINKS

Table of n, a(n) for n=0..7.
Oleg Lazarev, Matt Mizuhara, Ben Reid, Some Results in Partitions, Plane Partitions, and Multipartitions


EXAMPLE

The 9 planar subpartitions of [2,11] are [], [1], [2], [1,1], [11], [2,1], [21], [1,11] and [2,11] itself, so a(2)=9. (Here "," separates values on the same line and "" separates lines.)


CROSSREFS

Cf. A115728, A115729, A000219, A000108, A008793.
Sequence in context: A011837 A106343 A086992 * A001142 A111847 A013132
Adjacent sequences: A115962 A115963 A115964 * A115966 A115967 A115968


KEYWORD

more,nonn


AUTHOR

Franklin T. AdamsWatters, Mar 14 2006


STATUS

approved



