Recurrence Relations
Description: This quiz covers fundamental concepts and techniques related to recurrence relations, a core topic in combinatorics and discrete mathematics. | |
Number of Questions: 14 | |
Created by: Aliensbrain Bot | |
Tags: recurrence relations combinatorics discrete mathematics |
What is the general form of a linear homogeneous recurrence relation of order k?
Which of the following is a characteristic equation for the recurrence relation a_n = 3 * a_{n-1} - 2 * a_{n-2}?
What is the general solution to the recurrence relation a_n = 3 * a_{n-1} - 2 * a_{n-2} with initial conditions a_0 = 1 and a_1 = 2?
Which of the following is a recurrence relation for the Fibonacci sequence?
What is the generating function for the sequence {1, 2, 4, 8, 16, ...}?
Which of the following is a recurrence relation for the number of ways to climb n stairs, if you can take either one step or two steps at a time?
What is the asymptotic behavior of the solution to the recurrence relation a_n = 2 * a_{n-1} - 3 * a_{n-2} as n approaches infinity?
Which of the following is a recurrence relation for the number of ways to partition a set of n elements into k non-empty subsets?
What is the generating function for the sequence {1, 1, 2, 3, 5, 8, 13, ...}, where each term is the sum of the two previous terms?
Which of the following is a recurrence relation for the number of ways to make change for n cents using coins of denominations 1, 5, and 10 cents?
What is the asymptotic behavior of the solution to the recurrence relation a_n = 3 * a_{n-1} - 2 * a_{n-2} as n approaches infinity?
Which of the following is a recurrence relation for the number of ways to arrange n distinct objects in a row?
What is the generating function for the sequence {1, 4, 9, 16, 25, ...}?
Which of the following is a recurrence relation for the number of ways to color n balls using k colors, if each ball can be colored with any of the k colors?