a(n)=Number of Unique Matrix Products in (A+B+C+D)^n When [A,B]=0, etc.

[Paul D. Hanna]

Seqfans, 
      Below are 3 sequences that would also be of interest, that count
the 
number of unique non-commutative products in (A+B+C+D)^n. 
The desired sequences are defined below. 
   
(A1) "a(n) = number of unique matrix products in (A+B+C+D)^n  where 
commutator [A,B]=0 but neither A nor B commutes with C or D."  
  
(A2) "a(n) = number of unique matrix products in (A+B+C+D)^n  where 
commutators [A,B]=[C,D]=0 but neither A nor B commutes with C or D."  
 
(A3) "a(n) = number of unique matrix products in (A+B+C+D)^n  where 
commutators [A,B]=[A,C]=[B,C]=0 but D does not commute with A, B, or C." 
      
(The last one (A3) is a correction of a variation stated in my prior
email.)
 
If anyone could arrive at enough initial terms of these counts, it would
be nice!  
I do no know how to compute these sequences using PARI. 
Thanks, 
      Paul