n=3: 2:2/3, 3:2/3, 4:2/3
   E N_2 == (n-1)/n: True;  E N_3 == (n-1)(n^2-3n+3)/(n^2(n-2)): True
   sum = 2, sum i = 6
n=4: 2:3/4, 3:21/32, 4:33/64, 5:27/64, 6:3/8, 7:9/64, 8:9/64
   E N_2 == (n-1)/n: True;  E N_3 == (n-1)(n^2-3n+3)/(n^2(n-2)): True
   sum = 3, sum i = 12
n=5: 2:4/5, 3:52/75, 4:72/125, 5:1624/3375, 6:1346/3375, 7:1048/3375, 8:32/125, 9:193/1125, 10:92/675, 11:283/3375, 12:184/3375, 13:64/3375, 14:64/3375
   E N_2 == (n-1)/n: True;  E N_3 == (n-1)(n^2-3n+3)/(n^2(n-2)): True
   sum = 4, sum i = 20
n=6: 2:5/6, 3:35/48, 4:5/8, 5:7405/13824, 6:37915/82944, 7:55/144, 8:319295/995328, 9:780535/2985984, 10:1923875/8957952, 11:189275/1119744, 12:3614995/26873856, 13:305365/2985984, 14:694325/8957952, 15:746305/13436928, 16:357755/8957952, 17:232925/8957952, 18:152045/8957952, 19:43075/4478976, 20:625/110592, 21:625/331776, 22:625/331776
   E N_2 == (n-1)/n: True;  E N_3 == (n-1)(n^2-3n+3)/(n^2(n-2)): True
   sum = 5, sum i = 30
paper n=6 claims: 5/6, 35/48, 5/8, 7405/13824 -> 5/6 35/48 5/8 7405/13824
paper n=5 claim E N_5 = 1624/3375 -> 1624/3375
