# Tagged Questions

34 views

### Initial values appear from nothing

This answer says that any casual sequence of the kind $y_n = y_{n-1} + y_{n-2} + y_{n-3} + \ldots$ will stay constant-0 because $y_0$ is a sum of zeroes, so is $y_1$ and the rest of the sequence. I ...
76 views

230 views

### Fibonacci Generating Function of a Complex Variable

So I'm doing work on the Fibonacci Numbers, and I came across this problem for the generating function for the recursive fibonacci numbers. I have two questions: 1. Why is it useful to use a ...
230 views

### Generating Function of Even Fibonacci

I was posed the following question recently on an exam: Determine the generating function of the even-indexed Fibonacci numbers $F_{2n}$ given that the generating function of Fibonacci numbers is ...
279 views

### Expanding the generating function of the Fibonacci numbers to find a cute formula

$F_0=1$, $F_1=1$, $F_n=F_{n-1}+F_{n-2}$. The generating function is $-\frac{1}{x^2+x-1}$. I have to expand it to prove that $F_n=\sum_k\binom{k}{n-k}$. Could you help me please?
551 views

### On the generating function of the Fibonacci numbers

Let's define the Fibonacci numbers as $F_0=1$, $F_1=1$ and $F_n=F_{n-1}+F_{n-2}$. Using this recurrence I was able to calculate the generating function of the Fibonacci numbers to be ...
I am trying to solve identity involving binomials and fibbonaci numbers by using generating functions: \sum_{k=0}^n{n \choose k}{n+k\choose k}f_{k+1}=\sum_{k=0}^n{n \choose k}{n+k\choose ...