My solution for the sample test is:

 1  4^2 - 3^2 - 2^2 = 3
 2  3^2 - 2^2 - 1^2 = 4
 3  9^2 - 7^2 - 5^2 = 7
 4  14^2 - 11^2 - 8^2 = 11
 5  8^2 - 6^2 - 4^2 = 12
 6  6^2 - 4^2 - 2^2 = 16
 7  24^2 - 19^2 - 14^2 = 19
 8  13^2 - 10^2 - 7^2 = 20
 9  29^2 - 23^2 - 17^2 = 23
10  18^2 - 14^2 - 10^2 = 28
11  39^2 - 31^2 - 23^2 = 31
12  54^2 - 43^2 - 32^2 = 43
13  28^2 - 22^2 - 16^2 = 44
14  59^2 - 47^2 - 35^2 = 47
15  16^2 - 12^2 - 8^2 = 48
16  33^2 - 26^2 - 19^2 = 52
17  74^2 - 59^2 - 44^2 = 59
18  84^2 - 67^2 - 50^2 = 67
19  43^2 - 34^2 - 25^2 = 68
20  89^2 - 71^2 - 53^2 = 71
21  48^2 - 38^2 - 28^2 = 76
22  99^2 - 79^2 - 59^2 = 79
23  26^2 - 20^2 - 14^2 = 80
24  104^2 - 83^2 - 62^2 = 83
25  58^2 - 46^2 - 34^2 = 92

Can anybody confirm that? Thanks!