Number of Columns: 4
Number of Rows	Total Solutions
4	0
5	0
6	0
7	0
8	12
9	60
10	180
11	432
12	900
13	1,692
14	2,940
15	4,800
16	7,452
17	11,100
18	15,972
19	22,320
20	30,420
21	40,572
22	53,100
23	68,352
24	86,700
25	108,540
26	134,292
27	164,400
28	199,332
29	239,580
30	285,660

Equation (where "r" is the number of rows):

solutions = [(r-7)*(r-6)*(r-5)*(r-4)+(r-10)*(r-9)*(r-8)*(r-7)]/2

for r > 7