OFFSET
0,2
COMMENTS
This is a 2-dimensional analog of the Catalan numbers C_n (A000108). The number of subpartitions of the triangular partition [n,n-1,...,1] is C_{n+1}. The planar partition having its subpartitions counted is:
n n-1 ... 2 1
n-1 n-2 ... 1
... ...
2 1
1
LINKS
Oleg Lazarev, Matt Mizuhara, Ben Reid, Some Results in Partitions, Plane Partitions, and Multipartitions
EXAMPLE
The 9 planar subpartitions of [2,1|1] are [], [1], [2], [1,1], [1|1], [2,1], [2|1], [1,1|1] and [2,1|1] itself, so a(2)=9. (Here "," separates values on the same line and "|" separates lines.)
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Franklin T. Adams-Watters, Mar 14 2006
STATUS
approved