3.
In this problem we have a function defined recursively by:
g(0)=1, g(1)=2 and g(n+2)=2 g(n+1)+4 g(n) for all integers n?0.
Compute g(0), g(1), g(2), g(3) and g(4), by hand. Compute
g(1000) using a computer- again, you must explain the calcula-
tion. Write g(n) = 2<sup>n</sup> f(n). Compute the first few values of f. You
should get 1, 1, 2, 3, 5.... This should be a familiar sequence. Iden-
tify the sequence and prove your result.