xn+2 ≡ c0xn + c1xn+1 (mod 3) to generate the sequence 1, 1, 0, 2, 2, 0, 1, 1.
Set up and solve the matrix equation to find the coefficients c0 and c1.
This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.Because the operations are performed mod 3, the coefficients can be 0, 1 or 2.
We need only two equations to set the matrix (the coefficients can be also found by solving two recurrence relations as well).
The sequence is x0,x1, x2, x3…. is 1,1,0,2,2,0,1,1.
This means we need to plug into the provided recurrence relations the following:
1,1 |0 and 1,0|2
1,1|0 => x2=c0*x0+c1*x1 (mod 3)=> c0*1+c1*1=0 (mod 3)
1,0 |2 => x3=c0*x1+c1*x2 (mod 3)=> c0*1+c1*0=2 (mod 3)...