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3141
Kenneth Rosen Edition 7 Exercise 8.2 Question 38 (Page No. 526)
Find the characteristic roots of the linear homogeneous recurrence relation $a_{n} = 2a_{n-1} - 2a_{n-2}.$ [Note: These are complex numbers.] Find the solution of the recurrence relation in part $(A)$ with $a_{0} = 1\:\text{and}\: a_{1} = 2.$
Find the characteristic roots of the linear homogeneous recurrence relation $a_{n} = 2a_{n-1} - 2a_{n-2}.$ [Note: These are complex numbers.]Find the solution of the recu...
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Combinatory
kenneth-rosen
discrete-mathematics
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3142
Kenneth Rosen Edition 7 Exercise 8.2 Question 35 (Page No. 526)
Find the solution of the recurrence relation $a_{n} = 4a_{n-1} - 3a_{n-2} + 2^{n} + n + 3\:\text{with}\: a_{0} = 1\:\text{and}\: a_{1} = 4.$
Find the solution of the recurrence relation $a_{n} = 4a_{n-1} - 3a_{n-2} + 2^{n} + n + 3\:\text{with}\: a_{0} = 1\:\text{and}\: a_{1} = 4.$
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discrete-mathematics
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3143
Kenneth Rosen Edition 7 Exercise 8.2 Question 33 (Page No. 525)
Find all solutions of the recurrence relation $a_{n} = 4a_{n-1} - 4a_{n-2} + (n + 1)2^{n}.$
Find all solutions of the recurrence relation $a_{n} = 4a_{n-1} - 4a_{n-2} + (n + 1)2^{n}.$
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638
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May 5, 2020
Combinatory
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
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3144
Kenneth Rosen Edition 7 Exercise 8.2 Question 22 (Page No. 525)
What is the general form of the solutions of a linear homogeneous recurrence relation if its characteristic equation has the roots $-1, -1, -1, 2, 2, 5, 5, 7?$
What is the general form of the solutions of a linear homogeneous recurrence relation if its characteristic equation has the roots $-1, -1, -1, 2, 2, 5, 5, 7?$
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kenneth-rosen
discrete-mathematics
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recurrence-relation
descriptive
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3145
Kenneth Rosen Edition 7 Exercise 8.2 Question 21 (Page No. 525)
What is the general form of the solutions of a linear homogeneous recurrence relation if its characteristic equation has roots $1,1,1,1,−2,−2,−2,3,3,−4?$
What is the general form of the solutions of a linear homogeneous recurrence relation if its characteristic equation has roots $1,1,1,1,−2,−2,−2,3,3,−4?$
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313
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May 5, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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recurrence-relation
descriptive
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3146
Kenneth Rosen Edition 7 Exercise 8.2 Question 20 (Page No. 525)
Find the general form of the solutions of the recurrence relation $a_{n} = 8a_{n−2} − 16a_{n−4}.$
Find the general form of the solutions of the recurrence relation $a_{n} = 8a_{n−2} − 16a_{n−4}.$
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317
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May 3, 2020
Combinatory
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
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3147
Kenneth Rosen Edition 7 Exercise 8.2 Question 19 (Page No. 525)
Solve the recurrence relation $a_{n} = −3a_{n−1} − 3a_{n−2} − a_{n−3}\:\text{with}\: a_{0} = 5, a_{1} = −9,\:\text{and}\: a_{2} = 15.$
Solve the recurrence relation $a_{n} = −3a_{n−1} − 3a_{n−2} − a_{n−3}\:\text{with}\: a_{0} = 5, a_{1} = −9,\:\text{and}\: a_{2} = 15.$
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May 3, 2020
Combinatory
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discrete-mathematics
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recurrence-relation
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1
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3148
Kenneth Rosen Edition 7 Exercise 8.2 Question 18 (Page No. 525)
Solve the recurrence relation $a_{n} = 6a_{n−1} − 12a_{n−2} + 8a_{n−3} \:\text{with}\: a_{0} = −5, a_{1} = 4,\: \text{and}\: a_{2} = 88.$
Solve the recurrence relation $a_{n} = 6a_{n−1} − 12a_{n−2} + 8a_{n−3} \:\text{with}\: a_{0} = −5, a_{1} = 4,\: \text{and}\: a_{2} = 88.$
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May 3, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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recurrence-relation
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3149
Kenneth Rosen Edition 7 Exercise 8.2 Question 15 (Page No. 525)
Find the solution to $a_{n} = 2a_{n−1} + 5a_{n−2} − 6a_{n−3}\: \text{with}\: a_{0} = 7, a_{1} = −4,\:\text{and}\: a_{2} = 8.$
Find the solution to $a_{n} = 2a_{n−1} + 5a_{n−2} − 6a_{n−3}\: \text{with}\: a_{0} = 7, a_{1} = −4,\:\text{and}\: a_{2} = 8.$
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discrete-mathematics
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recurrence-relation
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3150
Kenneth Rosen Edition 7 Exercise 8.2 Question 14 (Page No. 525)
Find the solution to $a_{n} = 5a_{n−2}− 4a_{n−4} \:\text{with}\: a_{0} = 3, a_{1} = 2, a_{2} = 6, \:\text{and}\: a_{3} = 8.$
Find the solution to $a_{n} = 5a_{n−2}− 4a_{n−4} \:\text{with}\: a_{0} = 3, a_{1} = 2, a_{2} = 6, \:\text{and}\: a_{3} = 8.$
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3151
Kenneth Rosen Edition 7 Exercise 8.2 Question 13 (Page No. 525)
Find the solution to $a_{n} = 7a_{n−2} + 6a_{n−3}\:\text{with}\: a_{0} = 9, a_{1} = 10, \text{and}\: a_{2} = 32.$
Find the solution to $a_{n} = 7a_{n−2} + 6a_{n−3}\:\text{with}\: a_{0} = 9, a_{1} = 10, \text{and}\: a_{2} = 32.$
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282
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May 3, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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recurrence-relation
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3152
Kenneth Rosen Edition 7 Exercise 8.2 Question 12 (Page No. 525)
Find the solution to $a_{n} = 2a_{n−1} + a_{n−2} − 2a_{n−3} \:\text{for}\: n = 3, 4, 5,\dots, \:\text{with}\: a_{0} = 3, a_{1} = 6, \:\text{and}\: a_{2} = 0.$
Find the solution to $a_{n} = 2a_{n−1} + a_{n−2} − 2a_{n−3} \:\text{for}\: n = 3, 4, 5,\dots, \:\text{with}\: a_{0} = 3, a_{1} = 6, \:\text{and}\: a_{2} = 0.$
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272
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May 3, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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recurrence-relation
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3153
Kenneth Rosen Edition 7 Exercise 8.2 Question 3 (Page No. 524)
Solve these recurrence relations together with the initial conditions given. $a_{n} = 2a_{n−1}\:\text{for}\: n \geq 1, a_{0} = 3$ $a_{n} = a_{n−1} \:\text{for}\: n \geq 1, a_{0} = 2$ ... $a_{n} = a_{n−2} /4 \:\text{for}\: n \geq 2, a_{0} = 1, a_{1} = 0$
Solve these recurrence relations together with the initial conditions given.$a_{n} = 2a_{n−1}\:\text{for}\: n \geq 1, a_{0} = 3$ $a_{n} = a_{n−1} \:\text{for}\: n \ge...
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1.3k
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May 3, 2020
Combinatory
kenneth-rosen
discrete-mathematics
counting
recurrence-relation
descriptive
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3154
Kenneth Rosen Edition 7 Exercise 8.2 Question 2 (Page No. 524)
Determine which of these are linear homogeneous recurrence relations with constant coefficients. Also, find the degree of those that are. $a_{n} = 3a_{n-2}$ $a_{n} = 3$ $a_{n} = a^{2}_{n−1}$ $an = a_{n−1} + 2a_{n−3}$ $an = a_{n−1}/n$ $an = a_{n−1} + a_{n−2} + n + 3$ $a_{n} = 4a_{n−2} + 5a_{n−4} + 9a_{n−7}$
Determine which of these are linear homogeneous recurrence relations with constant coefficients. Also, find the degree of those that are.$a_{n} = 3a_{n-2}$ $a_{n} = 3$ $a...
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May 3, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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recurrence-relation
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3155
Kenneth Rosen Edition 7 Exercise 8.2 Question 1 (Page No. 524)
Determine which of these are linear homogeneous recurrence relations with constant coefficients. Also, find the degree of those that are. $a_{n} = 3a_{n−1} + 4a_{n−2} + 5a_{n−3}$ $a_{n} = 2na_{n−1} + a_{n−2}$ $a_{n} = a_{n−1} + a_{n−4}$ $a_{n} = a_{n−1} + 2 $ $a_{n} = a^{2}_{n−1} + a_{n−2} $ $a_{n} = a_{n−2}$ $a_{n} = a_{n−1} + n$
Determine which of these are linear homogeneous recurrence relations with constant coefficients. Also, find the degree of those that are.$a_{n} = 3a_{n−1} + 4a_{n−2} ...
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4.8k
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May 3, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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recurrence-relation
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3156
Kenneth Rosen Edition 7 Exercise 8.1 Question 21 (Page No. 511)
Find the recurrence relation satisfied by $R_{n},$ where $R_{n}$ is the number of regions that a plane is divided into by $n$ lines, if no two of the lines are parallel and no three of the lines go through the same point. Find $R_{n}$ using iteration.
Find the recurrence relation satisfied by $R_{n},$ where $R_{n}$ is the number of regions that a plane is divided into by $n$ lines, if no two of the lines are parallel a...
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1.1k
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asked
May 2, 2020
Combinatory
kenneth-rosen
discrete-mathematics
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descriptive
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1
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3157
Kenneth Rosen Edition 7 Exercise 8.1 Question 13 (Page No. 511)
A string that contains only $0s, 1s,$ and $2s$ is called a ternary string. Find a recurrence relation for the number of ternary strings of length $n$ that do not contain two consecutive $0s.$ What are the initial conditions? How many ternary strings of length six do not contain two consecutive $0s?$
A string that contains only $0s, 1s,$ and $2s$ is called a ternary string.Find a recurrence relation for the number of ternary strings of length $n$ that do not contain t...
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May 2, 2020
Combinatory
kenneth-rosen
discrete-mathematics
counting
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2
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3158
Kenneth Rosen Edition 7 Exercise 8.1 Question 11 (Page No. 511)
Find a recurrence relation for the number of ways to climb n stairs if the person climbing the stairs can take one stair or two stairs at a time. What are the initial conditions? In how many ways can this person climb a flight of eight stairs?
Find a recurrence relation for the number of ways to climb n stairs if the person climbing the stairs can take one stair or two stairs at a time.What are the initial cond...
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378
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May 2, 2020
Combinatory
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discrete-mathematics
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1
answer
3159
Kenneth Rosen Edition 7 Exercise 8.1 Question 10 (Page No. 511)
Find a recurrence relation for the number of bit strings of length $n$ that contain the string $01$. What are the initial conditions? How many bit strings of length seven contain the string $01?$
Find a recurrence relation for the number of bit strings of length $n$ that contain the string $01$.What are the initial conditions?How many bit strings of length seven c...
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409
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asked
May 1, 2020
Combinatory
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3160
Kenneth Rosen Edition 7 Exercise 6.6 Question 13 (Page No. 438)
List all $3$-permutations of $\{1, 2, 3, 4, 5\}.$
List all $3$-permutations of $\{1, 2, 3, 4, 5\}.$
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May 1, 2020
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