Please explain briefly Consider strings of characters each c

Please explain briefly?

Consider strings of characters, each character being a, b. or c, that contain an odd number of as. Let Sn be the number of such strings having length n. Which of the following is true? Sn = S_n-1 + S_n-2 Sn = 2 . S_n-1 + S_n-2 Sn = S_n-1 + (3^n-1 - S_n_1) S_n = 2 . S_n-1 + (3^n-1 - S_n-l)

Solution

As the string contains only odd numbers

Option a being sum of two odd numbers is even hence false

Option B 2(odd)+odd = odd hence true.