fibonacci

Let $G$ be an undirected graph, which is a path on 8 vertices. The number of matchings in $G$ is $\_\_\_\_$ (answer in integer)

Let $${a_n}$$ be the number of $$n$$-bit strings that do NOT contain two consecutive $$1s.$$ Which one of the following is the recurrence relation for $${a_n}$$?

A pennant is a sequence of numbers, each number being 1 or 2. An n-pennant is a sequence of numbers with sum equal to n. For example, (1,1,2) is a 4-pennant. The set of all possibl...

Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contains no consecutive $$0s$$. Which of the following recurrences does $${x_n}$$ satisfy?

Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contain no consecutive $$0s$$. The value of $${x_5}$$ is

What is the generating function G (z) for the sequence of Fibonacci numbers?