Formula for (iterative?) series?

[NotLKH]

hmmm,

I'm puzzled.

Lets say I have:

X₀ = 1, X₁ = 2, and:

X_i+2 = X_i+1 + 2*X_i + 3

This forms the series:
1, 2, 7, 14, 31, 62, ...

So,

When i is even,
X_i = 1 + 2*(4^(i/2)-1)

and when i is odd,
X_i = 2 + 4*(4^((i-1)/2)-1)

But, what is X_i when i <> integer, ie, perhaps when i = 1.6?