4
votes
4answers
1k views

Closed form solution of Fibonacci-like sequence

Could someone please tell me the closed form solution of the equation below. $$F(n) = 2F(n-1) + 2F(n-2)$$ $$F(1) = 1$$ $$F(2) = 3$$ Is there any way it can be easily deduced if the closed form ...
7
votes
8answers
829 views

Need help deriving recurrence relation for even-valued Fibonacci numbers.

That would be every third Fibonacci number, e.g. $0, 2, 8, 34, 144, 610, 2584, 10946,...$ Empirically one can check that: $a(n) = 4a(n-1) + a(n-2)$ where $a(-1) = 2, a(0) = 0$. If $f(n)$ is ...
1
vote
1answer
101 views

Recovering two first terms from sequence $f(n)=f(n-1)+f(n-2)$

Having very simple sequence $f(n)=f(n-1)+f(n-2)$ and having $n-th$ term given how can we calculate from which first two terms this $n-th$ term came? I know the answer can be not unique so highest ...