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8. Carrot the Cat Carrot the cat likes taking naps in one of four locations: the rug, the bed, the ledge, and the sink. Carrot has the following conditions: • He will not sleep in the sink twice in a row • He will sleep on the ledge only if he slept on the rug the previous time Let L(n) be the number of possible sequences of locations for n naps, where n ≥0. (a) Give a recurrence relation for L(n). (b) Give the initial conditions for your recurrence. Include

8. Carrot the Cat Carrot the cat likes taking naps in one of four locations: the rug, the bed, the ledge, and the sink. Carrot has the following conditions: • He will not sleep in the sink twice in a row • He will sleep on the ledge only if he slept on the rug the previous time Let L(n) be the number of possible sequences of locations for n naps, where n ≥0. (a) Give a recurrence relation for L(n). (b) Give the initial conditions for your recurrence. Include

Advanced Engineering Mathematics
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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8. Carrot the Cat Carrot the cat likes taking naps in one of four locations: the rug, the bed, the ledge, and the sink. Carrot has the following conditions: • He will not sleep in the sink twice in a row • He will sleep on the ledge only if he slept on the rug the previous time Let L(n) be the number of possible sequences of locations for n naps, where n ≥0. (a) Give a recurrence relation for L(n). (b) Give the initial conditions for your recurrence. Include only the minimum necessary conditions.
Transcribed Image Text:8. Carrot the Cat Carrot the cat likes taking naps in one of four locations: the rug, the bed, the ledge, and the sink. Carrot has the following conditions: • He will not sleep in the sink twice in a row • He will sleep on the ledge only if he slept on the rug the previous time Let L(n) be the number of possible sequences of locations for n naps, where n ≥0. (a) Give a recurrence relation for L(n). (b) Give the initial conditions for your recurrence. Include only the minimum necessary conditions.
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