A 2 × n checkerboard is to be tiled using three types of tiles. The first tile is a white 1 × 1 square tile. The second...

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Question

A 2 × n checkerboard is to be tiled using three types of tiles. The first tile is a

white 1 × 1 square tile. The second tile is a red 2 × 2 tile and the third one is a black 2 × 2 tile.

Let t(n) denote the number of tilings of the 2 × n checkerboard using white, red and black tiles.

(a) Find a recursive formula for t(n) and use it to determine t(7).

(b) Let f(n) = c1*2^n+ c2(-1)^n. Determine c1and c2so that f(0) = f(1) = 1.

(c) Prove that f(n) satisfies the same recurrence relation as t(n).

(d) Can we now conclude that f(n) = t(n) for all positive integers n?

Problem 7. A 2 × n checkerboard is to be tiled using three types of tiles. The first tile is a white 1 × 1 square tile. The s

math Advanced-Math

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