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Give a recursive formula for the function g(n) that counts the number of ternary strings of...
Consider binary strings with n digits (for example, if n = 4 some of the possible...
Consider binary strings with n digits (for example, if n = 4 some of the possible strings are 0011, 1010, 1101, etc.) Let z be the number of binary strings of length n that do not contain the substring 000 Find a recurrence relation for z You are not required to find a closed form for this recurrence
Consider binary strings with n digits (for example, if n = 4 some of the possible strings are 0011, 1010, 1101, etc.)...
) Find a recurrence relation for the number of ternary strings of length n≥1 that do...
) Find a recurrence relation for the number of ternary strings of length n≥1 that do not contain two or more consecutive 2s. (Hint: A ternary string consists of 0s, 1s, and 2s.)
Problem 3. A ternary string is a sequence of O's, 1's and 2's. Just like a...
Problem 3. A ternary string is a sequence of O's, 1's and 2's. Just like a bit string, but with three symbols 0,1 and 2. Let's call a ternary string good provided it never contains a 2 followed immediately by a 0, i.e., does not contain the substring 20. Let Go be the number of good strings of length n. For example, G_1=3, and G. = 8 (since of the 9 ternary strings of length 2, only one is not...
explain why the recurrence relation for number of ternary strings of length n contains "01" 7....
explain why the recurrence relation for number of ternary strings
of length n contains "01"
7. (10 points) Extra credit: Explain why the recurrence relation for number of ternary strings of length n that contain "01" is bn = 3n-1-bn-2 +31-2?
3. (10 points) Let T = {A, B,C), and let tn be the number of T-strings...
3. (10 points) Let T = {A, B,C), and let tn be the number of T-strings of length n which do not contain AA or BA as substrings. Find a recurrence for tn, and then use that to find a closed-form (i.e. non-recursive) formula for tn.
Discrete Mathematics 7. (15 points) Let an be the number of length n ({ne Zin 20})...
Discrete Mathematics
7. (15 points) Let an be the number of length n ({ne Zin 20}) ternary strings (strings made up of {0, 1, 2), ex. 01211120002) that contain two consecutive digits that are the same. For example, a = 3 since the only ternary strings of length 2 with matching consecutive digits are 00, 11, and 22. Also, a, = 0, since in order to have consecutive matching digits, a string must be of length at least two. a....
Let Σ = {0, 1). (a) Give a recursive definition of Σ., the set of strings from the alphabet Σ. (b) Prove that for every n E N there are 2" strings of length n in '. (c) Give a recursive d...
Let Σ = {0, 1). (a) Give a recursive definition of Σ., the set of strings from the alphabet Σ. (b) Prove that for every n E N there are 2" strings of length n in '. (c) Give a recursive definition of I(s), the length of a string s E Σ For a bitstring s, let O(s) and I(s) be number of zeroes and ones, respectively, that occur in s. So for example if s = 01001, then 0(s)...
Let n be an even number. How many ternary strings (i.e. strings over the alphabet 10,...
Let n be an even number. How many ternary strings (i.e. strings over the alphabet 10, 1,2]) of length n are there in which the only places that zeroes can appear are in the odd-numbered positions?
Give a recursive formula t(n) for the sequence of central binomial coefficients (m), [,2,6, 20,70,...] of...
Give a recursive formula t(n) for the sequence of central binomial coefficients (m), [,2,6, 20,70,...] of the form where a and b are real numbers and Cn is the nth Catalan number. You do not need to prove that your formula is correct.
Give a recursive formula s(n) for the sequence of squares [1,4,9, 16, 25,...] of the form...
Give a recursive formula s(n) for the sequence of squares [1,4,9, 16, 25,...] of the form s(n 1) as(n) + bs(n - 1) +cs(n-2), where a,b and c are real numbers. You do not need to prove that your formula is correct.
Consider binary strings with n digits (for example, if n = 4 some of the possible strings are 0011, 1010, 1101, etc.) Let z be the number of binary strings of length n that do not contain the substring 000 Find a recurrence relation for z You are not required to find a closed form for this recurrence
Consider binary strings with n digits (for example, if n = 4 some of the possible strings are 0011, 1010, 1101, etc.)...
Problem 3. A ternary string is a sequence of O's, 1's and 2's. Just like a bit string, but with three symbols 0,1 and 2. Let's call a ternary string good provided it never contains a 2 followed immediately by a 0, i.e., does not contain the substring 20. Let Go be the number of good strings of length n. For example, G_1=3, and G. = 8 (since of the 9 ternary strings of length 2, only one is not...
explain why the recurrence relation for number of ternary strings
of length n contains "01"
7. (10 points) Extra credit: Explain why the recurrence relation for number of ternary strings of length n that contain "01" is bn = 3n-1-bn-2 +31-2?
3. (10 points) Let T = {A, B,C), and let tn be the number of T-strings of length n which do not contain AA or BA as substrings. Find a recurrence for tn, and then use that to find a closed-form (i.e. non-recursive) formula for tn.
Discrete Mathematics
7. (15 points) Let an be the number of length n ({ne Zin 20}) ternary strings (strings made up of {0, 1, 2), ex. 01211120002) that contain two consecutive digits that are the same. For example, a = 3 since the only ternary strings of length 2 with matching consecutive digits are 00, 11, and 22. Also, a, = 0, since in order to have consecutive matching digits, a string must be of length at least two. a....
Let Σ = {0, 1). (a) Give a recursive definition of Σ., the set of strings from the alphabet Σ. (b) Prove that for every n E N there are 2" strings of length n in '. (c) Give a recursive definition of I(s), the length of a string s E Σ For a bitstring s, let O(s) and I(s) be number of zeroes and ones, respectively, that occur in s. So for example if s = 01001, then 0(s)...
Let n be an even number. How many ternary strings (i.e. strings over the alphabet 10, 1,2]) of length n are there in which the only places that zeroes can appear are in the odd-numbered positions?
Give a recursive formula t(n) for the sequence of central binomial coefficients (m), [,2,6, 20,70,...] of the form where a and b are real numbers and Cn is the nth Catalan number. You do not need to prove that your formula is correct.
Give a recursive formula s(n) for the sequence of squares [1,4,9, 16, 25,...] of the form s(n 1) as(n) + bs(n - 1) +cs(n-2), where a,b and c are real numbers. You do not need to prove that your formula is correct.
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