MathDB

Prove that the numbers

A,B

and

C

are equal, where: -

A=

number of ways that we can cover a

2 \times n

rectangle with

2 \times 1

retangles. -

B=

number of sequences of ones and twos that add up to

n

C= \sum^m_{k=0} \binom{m + k}{2 \cdot k}

n = 2 \cdot m,

and -

C= \sum^m_{k=0} \binom{m + k + 1}{2 \cdot k + 1}

n = 2 \cdot m + 1.

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