A set of blocks contains blocks of heights 1, 2, and 4 centimeters. Imagine constructing

Chapter 5, Problem 40

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A set of blocks contains blocks of heights 1, 2, and 4 centimeters. Imagine constructing towers by piling blocks of different heights directly on top of one another. (A tower of height 6 cm could be obtained using six 1-cm blocks, three 2-cm blocks one 2-cm block with one 4-cm block on top, one 4-cm block with one 2-cm block on top, and so forth.) Let t be the number of ways to construct a tower of height n cm using blocks from the set. (Assume an unlimited supply of blocks of each size.) Find a recurrence relation for \(t_{1}, t_{2}, t_{3}\), . . ..

Text Transcription:

t_1, t_2, t_3