6. Now let D represent the number of domino tilings of a 3 x n checkerboard....
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
6. Now let D₁ represent the number of domino tilings of a 3 x n checkerboard. It is considerably trickier to come up with a recurrence relation in this case, though the ideas involved are similar. (a) List (by drawing them) three possibilities for how the rightmost column of a 3 x n board can be covered. (b) Let C₁, be the number of a domino tilings of a 3 x n board with one missing corner. By considering the options you gave in part (a), explain why Dn = Dn-2 +2Cn-1. (c) Now start with a board missing a corner (say the top right corner). Again consider the possibilities for how to cover the rightmost column, and use your analysis to show that Cn Dn-1 + Cn-2- - = (d) Combine the results of (b) and (c) to show that Dn 4Dn-2 - Dn-4. (e) Find initial conditions Do and D₂. What is D, for any odd value of n? 6. Now let D₁ represent the number of domino tilings of a 3 x n checkerboard. It is considerably trickier to come up with a recurrence relation in this case, though the ideas involved are similar. (a) List (by drawing them) three possibilities for how the rightmost column of a 3 x n board can be covered. (b) Let C₁, be the number of a domino tilings of a 3 x n board with one missing corner. By considering the options you gave in part (a), explain why Dn = Dn-2 +2Cn-1. (c) Now start with a board missing a corner (say the top right corner). Again consider the possibilities for how to cover the rightmost column, and use your analysis to show that Cn Dn-1 + Cn-2- - = (d) Combine the results of (b) and (c) to show that Dn 4Dn-2 - Dn-4. (e) Find initial conditions Do and D₂. What is D, for any odd value of n?
Expert Answer:
Answer rating: 100% (QA)
I dont have visual abilities to draw or identify images but I can guide you through the process of answering the questions a To cover the rightmost co... View the full answer
Related Book For
Introduction to Probability and Statistics
ISBN: 978-1133103752
14th edition
Authors: William Mendenhall, Robert Beaver, Barbara Beaver
Posted Date:
Students also viewed these mathematics questions
-
How would you go about attempting to come up with the probability of a super- event or the probability of a unique- event? What factors would you consider?
-
Let X and Y represent the number of Dell and HP laptop computers, respectively, sold per month from online sites. The file S04_28.xlsx contains the probabilities of various combinations of monthly...
-
For this network design assignment, you are free to come up with a fictional midsized company engaged in a dot-com business for which you will select the business focus. The company can be a...
-
The cylinder in the figure has a radius of 2 ft and rolls without slipping on the horizontal surface. The bar AB is attached to the periphery of the cylinder by a pin at point A. The other end of the...
-
Define order triage and explain how it can impact order processing.
-
Graphically solve the following problem: (a) What is the optimal solution? (b) Change the right-hand side of constraint 1 to 11 (instead of 10) and resolve the problem. How much did the profit...
-
Lola Stroud invests \($30,000.00\) in a partnership. Her partner, Juan Santo, invests \($50,000.00\). Miss Stroud has 10 years' experience in a similar business; Mr. Santo has no experience. Miss...
-
Review the Diversity Competency feature entitled Chubbs Business Case for Diversity. In what three ways do you agree and/or disagree with this business case for diversity?
-
6. Produce the relay logic circuit and the equivalent ladder logic program for a motor Start/Stop operation. L1 L2 START STOP OL M # M M HH HH M Rung R Rail
-
On January 1, 2023, Pulaski, Incorporated, acquired a 60 percent interest in the common stock of Sheridan, Incorporated, for $392,400. Sheridan's book value on that date consisted of common stock of...
-
P & B Ltd manufactures and sells pens. The total fixed costs is $456,500 per year. The price per unit is $18.75; the variable costs per unit is $13.50; the income tax rate is 35%; and the net profit,...
-
What are the criteria for a rigid body to undergo planar motion?
-
Monochromatic \(647-\mathrm{nm}\) light is incident on a single slit. If the diffraction pattern is cast on a screen \(3.0 \mathrm{~m}\) from the slit, and the \(n=3\) dark fringe is \(2.5...
-
What concerns was the ICWA intended to redress?
-
Blue laser light \((\lambda=476.5 \mathrm{~nm})\) passes through a slit of width \(a=0.150 \mathrm{~mm}\). On a screen a distance \(L=2.500 \mathrm{~m}\) from the slit, what is the linear distance...
-
What does it mean to terminate parental rights? What must the state prove at a termination hearing?
-
TCP/IP and Network TroubleshootingPreparation Instructions Compare common LAN network cables and connectors. Describe the pros and cons of each as well as their likely applications. Describe...
-
An item of depreciable machinery was acquired on 1 July 2009 for $120,000 by cash It is expected to have a useful life of 10 years and zero salvage value On 1 July 2012, it was decided to revalue the...
-
During the inaugural season of Major League Soccer in the United States, the medical teams documented 256 injuries that caused a loss of participation time to the player. The results of this...
-
Even though we know it may not be good for us, many Americans really enjoy their fast food! A survey conducted by Pew Research Center graphically illustrated our penchant for eating out, and in...
-
A random sample of size n = 50 is selected from a binomial distribution with population proportion p = .7. a. What will be the approximate shape of the sampling distribution of ? b. What will be the...
-
Where do the following accounts (and their balances) appear in the balance sheet? a. Dividends Payable-Common Stock b. Stock Dividend Distributable
-
What are the different sources of paid-in capital?
-
Bleaker Company declares and pays its annual dividend near the end of its fiscal year. For the current year, Bleaker's dividend payout ratio was 40 percent, its earnings per common share were \(\$...
Study smarter with the SolutionInn App