In a, it is concluded that when k is odd,

b(k+ 1)-b(k- 1)= 2^(k- 1)+ 1(#)

If n is odd, then when k=n

b(n+ 1)-b(n- 1)= 2^(n- 1)+ 1

And when k=n+ 1, k is not an odd number and cannot be substituted into the (#) formula.

So we can't get b (n+2)-b (n) = 2 n+ 1.