a(n)=Number of Unique Matrix Products in (A+B+C)^n When {A,B}=0

[Paul D. Hanna]

Seqfans,
       Excuse me, this is obviously incorrect:
> Example:  if A,B anti-commute, {A,B}=AB+BA=0,  
> then (A+B)^n has 2^[(n+1)/2] distinct parts (g.f. (1+2x)/(1-2x^2)). 
I think the formula I gave was for total number of parts, not distinct.
Distinct number of parts I believe will be [(n+1)/2], 
about half that if A,B were to commute. 
  
The number of total parts becomes interesting when anti-commuting letters
are among among commuting letters; 
example, what is:
  
a(n) = number of parts, not necessarily distinct, in (A+B+C)^n 
where A,B, anti-commute, while A,B commute with C:  
{A,B}=0, [A,C] !=0, [B,C] !=0. 
  
Paul