For example,
a(0) = 

+ 

+ 

+ ... = e 1 
a(1) = 

+ 

+ 

+ ... = 2e 3 
a(2) = 

+ 

+ 

+ ... = 

e 6 
It can be shown that a(n) is of the form 

for integers A(n) and B(n). 
For example a(10) = 

. 
Find A(10^{9}) + B(10^{9}) and give your answer mod 77 777 777.
These problems are part of Project Euler and are licensed under CC BYNCSA 2.0 UK