A ternary string is a sequence of 0's, 1's and 2's. Just like a bit string, but with three symbols. Let's call a ternary string good provided it never contains a 2 followed immediately by a 0. Let Gn be the number of good strings of length n. For example, G1=3 and G2=8 (since of the 9 ternary strings of length 2, only one is not good). Find, with justification, a recursive formula for Gn , and use it to compute G5. Hint: Consider three cases: the last digit is a 0, a 1, or a 2. Two of these should be easy to count, but strings ending in 0 cannot be proceeded by a 2, so require a little more work.
A ternary string is a sequence of 0's, 1's and 2's. Just like a bit string, but with three symbols. Let's call a ternary string good provided it never contains a 2 followed immediately by a 0. Let Gn be the number of good strings of length n. For example, G1=3 and G2=8 (since of the 9 ternary strings of length 2, only one is not good). Find, with justification, a recursive formula for Gn , and use it to compute G5. Hint: Consider three cases: the last digit is a 0, a 1, or a 2. Two of these should be easy to count, but strings ending in 0 cannot be proceeded by a 2, so require a little more work.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A ternary string is a sequence of 0's, 1's and 2's. Just like a bit string, but with three symbols.
Let's call a ternary string good provided it never contains a 2 followed immediately by a 0. Let Gn be the number of good strings of length n. For example, G1=3 and G2=8 (since of the 9 ternary strings of length 2, only one is not good).
Find, with justification, a recursive formula for Gn , and use it to compute G5.
Hint:
Consider three cases: the last digit is a 0, a 1, or a 2. Two of these should be easy to count, but strings ending in 0 cannot be proceeded by a 2, so require a little more work.
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