Stuart E Anderson: That should read; 
41 {3x3 for A>B & A=B} - 10 {3x3  for  A=B} =31 , 
2*31+10 = 72 {3x3 for  (A>B) & (A=B) & (B>A) & (A*B=A+B) }
1909 {4x4  for A>B & A=B} - 58 {4x4 for A=B} =1851 ,
 2*1851+58 = 3760 {4x4  for  (A>B) & (A=B) & (B>A) & (A*B=A+B)}

Stuart E Anderson: I think I had ordered and unordered confused.

Andrew Howroyd: these are ordered so the name is correct.

Stuart E Anderson: Yes

Stuart E Anderson: I've counted ordered pairs.
41 {3x3 A*B=A+B, for A>B, A!=B} - 10 {3x3 A=B} =31 , 2*31+10 = 72 {A*B=A+B}
1909 {4x4 A*B=A+B, for A>B, A!=B} - 58 {4x4 A=B} =1851 , 2*1851+58 = 3760 {A*B=A+B}
If I double my counts for {A>B, A!=B} I get counts for all pairs {A!=B}, if I add the counts for {A=B} in, its equivalent to your counts.
Should the sequence name read 'unordered' rather than ordered?

Stuart E Anderson: My code is awful. I agree. I have nearly finished writing a much better program. I hope to have it ready and tested tonight.  I work long shifts in an industry unrelated to maths or computers and I lack a lot of knowledge and training.  Thank you for being patient with me.

Andrew Howroyd: no worries - its good to have a hobby outside of work! By the time you get to my age you will wonder why you didn't retire sooner.

Stuart E Anderson: I've written and uploaded my program.   I get terms 1,2,41,1909.  For A == B I have 1,2,10,58.  I havnt looked at your code yet.

Andrew Howroyd: I have added my program.

Stuart E Anderson: I have added links to the programs for my 3x3 and 4x4 solutions.  My results have the sequence as 1,2,41,1972.  which is still a new sequence.

Stuart E Anderson: The programs print out all the A B  matrices, their sum|product C, decimals for A B and a list of the unique A B decimals and lastly summary stats.

Stuart E Anderson: Is it sensible to have a sequence of unordered pairs, and another sequence of ordered pairs?

Andrew Howroyd: Before looking into unordered pairs, we should address the issue of why I have 3760 solutions. Your C++ program is unreadable and the fact that you have separate programs for a(3) and a(4) is a strong indicator of a bug.

Stuart E Anderson: ok.  I'll rewrite a single program 
The program is readable in a wide enough monitor.   Can I see how you got 3760?

Andrew Howroyd: The unreadability is that you have 32 variables and there is no way to be sure you don't have any typos. (nothing to do with monitor width). 
Indeed if you look carefully at the following lines
&&((e+u) == (e*q + f*n + g*y + h*ac))
 &&((f+v) == (e*r + f*o + g*z + h*ad))
&&((g+w) == (e*s + f*m + g*aa + h*ae))
&&((h+x) == (e*t + f*n + g*ab + h*af))

You will see that the multipliers after f are the wrong ones.

Andrew Howroyd: Should be f*u f*v f*w f*x ?

Stuart E Anderson: you're right. It seems Ive counted twice.

Andrew Howroyd: Can you check your value for a(4)? I get 3760

Stuart E Anderson: For 4x4 (1,0) matrices I get 1732 unique pairs, with 29 of those A = B

Stuart E Anderson: I converted the 1,0 matrix pairs to a 16 bit string then converted it to a decimal,
printed the larger of the two numbers of the pair first, kept a count if the numbers were equal, then sorted the list down to unique lines.

Stuart E Anderson: For 3x3 (1,0) matrices I now have 41 unique pairs, which includes 10 singleton pairs where A = B

Stuart E Anderson: correction  For 4x4 (1,0) matrices I get 1972 unique pairs, with 29 of those A = B

Alois P. Heinz: A060757: size of search space ...