OFFSET
0,3
COMMENTS
A000219 counts planar partitions of n, which are represented by arrays of positive integers A(r,c) that sum to n and are 2-way monotonic in the sense of A(r,c+1) <= A(r,c) and A(r+1,c) <= A(r,c). The sequence here imposes the additional constraint that the absolute difference between A(r,c) and any of the (up to 4) adjacent terms A(r+1,c), A(r-1,c), A(r,c+1) and A(r,c-1) is <=1.
EXAMPLE
a(6)=34 and A000219(6) = 48 differ by 14 because the following 48-34=14 plane partitions of 6 are not counted here:
3 1 1 1 (and its transpose)
.
4 1 1 (and its transpose)
.
3 1
1
1 (and its transpose)
.
3 1
1 1
.
3 1
2 (and its transpose)
.
4 2 (and its transpose
.
4 1
1
.
5 1 (and its transpose)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
R. J. Mathar, Jan 09 2015
STATUS
approved