Problem 114

Counting block combinations I

A row measuring seven units in length has red blocks with a minimum length of three units placed on it, such that any two red blocks (which are allowed to be different lengths) are separated by at least one black square. There are exactly seventeen ways of doing this.

![pe114](\images\pe114.png)

How many ways can a row measuring fifty units in length be filled?

NOTE: Although the example above does not lend itself to the possibility, in general it is permitted to mix block sizes. For example, on a row measuring eight units in length you could use red (3), black (1), and red (4).

方格组合计数I

用黑色方块和最短长度为3的红色方块摆成长度为7的一行，要求任意两个红色方块（长度可以不同）之间至少有一个黑色方块，恰好有17种不同的摆法。

![pe114](\images\pe114.png)

若要摆成长度为50的一行，有多少种不同的摆法？

注意：尽管上述样例没有混用不同长度的方格，但这样做是允许的。例如，要摆成长度为8的一行，你可以用红（3）、黑（1）、红（4）。