- #1
sjaguar13
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A set of blocks contains blocks of heights 1, 2, and 4 inches. Imagine constructing towers of piling block of different heights directly on top of one another. Let t(n) be the number of ways to construct a tower of height n inches. Find a recurrence relation for t(1), t(2), t(3)...
Here's what I got:
There are 5 ways to make a tower of 4 inches,
There are 6 ways to make a tower of 5 inches,
There are 10 ways to make a tower of 6 inches.
t(1) = 1, t(2) = 2, and t(3) = 4
t(k) = t(k-1) + t(k-2) - 1, k >= 4
Is that right? I would guess there should be a t(k-3) in there somewhere just because they give you three numbers.
Here's what I got:
There are 5 ways to make a tower of 4 inches,
There are 6 ways to make a tower of 5 inches,
There are 10 ways to make a tower of 6 inches.
t(1) = 1, t(2) = 2, and t(3) = 4
t(k) = t(k-1) + t(k-2) - 1, k >= 4
Is that right? I would guess there should be a t(k-3) in there somewhere just because they give you three numbers.