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explain why the recurrence relation for number of ternary strings
of length n contains "01"
7....
) 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.)
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....
Discrete mathematics 2) Let be eumber of ternary strings (of 0s, 1s and 2s) of length n that have no adjacent even digits. For example, so (the empty string), s3 (the strings 0, 1 and 2), while s2...
Discrete mathematics
2) Let be eumber of ternary strings (of 0s, 1s and 2s) of length n that have no adjacent even digits. For example, so (the empty string), s3 (the strings 0, 1 and 2), while s2 5: 01, 0, 12, 2 because the strings 00,02, 20, 22 are not allowed, as they have adjacent even digits. As another example, the string 10112 is allowed, while the strings 10012 and 120121 are not allowed (a) Find #3; (b) find...
Give a recursive formula for the function g(n) that counts the number of ternary strings of...
Give a recursive formula for the function g(n) that counts the number of ternary strings of length n that do not contain 2002 as a substring. You do not need to find a closed form solution for g(n).
(12 points) For each sequence described below, first find a recurrence relation for that sequence...
Discrete Math for COMP:
(12 points) For each sequence described below, first find a recurrence relation for that sequence and then solve your recurrence relation. (a) The sequence Sn where 80 = 0, si-l and, for n 〉 1, sn s the average of the previous two terms of the sequence. (b) The sequence bn whose nth term is the number of n-bit strings that don't have two zeros in a rovw (c) The sequence en whose nth term is...
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?
can someone help me with this two questions please thank you 4. Find a recurrence relation...
can someone help me with this two questions please
thank you
4. Find a recurrence relation (with initial conditions) for an, the number of ternary sequences of length n that do not contain three consecutive digits that are the same. That is, the patterns '000','111', 222 must not appear anywhere in the sequence. So, 0011012 is acceptable, but 000022 and 1000112 are not. 5. Elsa is making trains out of colored train cars: the red cars are 2 inches long,...
In the Island of Combinatorica, a valid drivers license of length n can be constructed in 3 ways:...
In the Island of Combinatorica, a valid drivers license of length n can be constructed in 3 ways: (a) Starting with A followed by any valid drivers license of length n -1 (b) Starting with one of the two-character strings 1A, 1B, 1C,1D, 1E, or 1F followed by any drivers license of length n-2 (c) Starting with 0 and followed by any ternary string (alphabet 0, 1,2]) of lengthn-1. Find a recurrence for the number g(n) of valid drivers licenses...
Discrete math 4. Popeye and Olive Oyl frequently send each other text messages that are just contiguous strings of the three emojis , , and . For instance, one particular length-5 emoji string might b...
Discrete math
4. Popeye and Olive Oyl frequently send each other text messages that are just contiguous strings of the three emojis , , and . For instance, one particular length-5 emoji string might be e (a) Find a recurrence relation for the number of possible length-n emoji strings that do not contain two consecutive winkey emojis, (b) What are the initial conditions for the recurrence relation? (c) Find a closed-form solution to the recurrence relation you found in part...
6. (10 points) Let Sn be the number of n-bit strings of O's and 1's that...
6. (10 points) Let Sn be the number of n-bit strings of O's and 1's that avoid the pattern "11". Find the recurrence relation for sm and find the solution for this recurrence relation.
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....
Discrete mathematics
2) Let be eumber of ternary strings (of 0s, 1s and 2s) of length n that have no adjacent even digits. For example, so (the empty string), s3 (the strings 0, 1 and 2), while s2 5: 01, 0, 12, 2 because the strings 00,02, 20, 22 are not allowed, as they have adjacent even digits. As another example, the string 10112 is allowed, while the strings 10012 and 120121 are not allowed (a) Find #3; (b) find...
Give a recursive formula for the function g(n) that counts the number of ternary strings of length n that do not contain 2002 as a substring. You do not need to find a closed form solution for g(n).
Discrete Math for COMP:
(12 points) For each sequence described below, first find a recurrence relation for that sequence and then solve your recurrence relation. (a) The sequence Sn where 80 = 0, si-l and, for n 〉 1, sn s the average of the previous two terms of the sequence. (b) The sequence bn whose nth term is the number of n-bit strings that don't have two zeros in a rovw (c) The sequence en whose nth term is...
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?
can someone help me with this two questions please
thank you
4. Find a recurrence relation (with initial conditions) for an, the number of ternary sequences of length n that do not contain three consecutive digits that are the same. That is, the patterns '000','111', 222 must not appear anywhere in the sequence. So, 0011012 is acceptable, but 000022 and 1000112 are not. 5. Elsa is making trains out of colored train cars: the red cars are 2 inches long,...
In the Island of Combinatorica, a valid drivers license of length n can be constructed in 3 ways: (a) Starting with A followed by any valid drivers license of length n -1 (b) Starting with one of the two-character strings 1A, 1B, 1C,1D, 1E, or 1F followed by any drivers license of length n-2 (c) Starting with 0 and followed by any ternary string (alphabet 0, 1,2]) of lengthn-1. Find a recurrence for the number g(n) of valid drivers licenses...
Discrete math
4. Popeye and Olive Oyl frequently send each other text messages that are just contiguous strings of the three emojis , , and . For instance, one particular length-5 emoji string might be e (a) Find a recurrence relation for the number of possible length-n emoji strings that do not contain two consecutive winkey emojis, (b) What are the initial conditions for the recurrence relation? (c) Find a closed-form solution to the recurrence relation you found in part...
6. (10 points) Let Sn be the number of n-bit strings of O's and 1's that avoid the pattern "11". Find the recurrence relation for sm and find the solution for this recurrence relation.
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