[seqfan] plane partitions into unrestricted integers of 2 colors

[David Newman]

I've tried this by hand and for n=1,2,3 I got the values 2, 10, 31 and I'm
not even sure of those.
In plane partitions the summands are non-increasing on rows and columns.
Each integer comes in two colors,, let's call them red and blue. so  for
n=1 the two partitions are 1r and  1b

For n=2 there are 10 partitions

2b     2r

(1b +  1b)  (1b + 1r) (1r+1b) (1r+ 1r)

(1b
+1b)

(1b
+1r)

(1r
+1b)

(1r
+1r)

Can someone program this counting process?