Number of Columns: 7
Number of Rows	Total Solutions
7	0
8	0
9	2
10	100
11	908
12	4,872
13	19,818
14	66,864
15	193,926
16	498,924
17	1,165,544
18	2,517,036
19	5,089,430
20	9,731,908
21	17,735,888
22	30,999,920
23	52,234,274
24	85,210,284
25	135,059,570
26	208,627,984
27	314,889,330
28	465,423,908
29	674,966,914
30	962,031,720
31	1,349,613,074
32	1,865,975,260

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

solutions = r^7 -85r^6 +3329r^5 -77911r^4 +1175240r^3 -11392990r^2 +65448630r -171006180

for r > 23