Problem 116

Red, green or blue tiles

A row of five black square tiles is to have a number of its tiles replaced with coloured oblong tiles chosen from red (length two), green (length three), or blue (length four).

If red tiles are chosen there are exactly seven ways this can be done.

![pe116_1](\images\pe116_1.png)

If green tiles are chosen there are three ways.

![pe116_2](\images\pe116_2.png)

And if blue tiles are chosen there are two ways.

![pe116_3](\images\pe116_3.png)

Assuming that colours cannot be mixed there are 7 + 3 + 2 = 12 ways of replacing the black tiles in a row measuring five units in length.

How many different ways can the black tiles in a row measuring fifty units in length be replaced if colours cannot be mixed and at least one coloured tile must be used?

NOTE: This is related to Problem 117.

红色、绿色或蓝色的地砖

将一行五块黑色方形地砖的一部分替换成红色（长度为2）、绿色（长度为3）或蓝色（长度为4）的地砖。

如果只使用红色地砖，一共有7种不同的替换方式。

![pe116_1](\images\pe116_1.png)

如果只使用绿色地砖，一共有3种不同的替换方式。

![pe116_2](\images\pe116_2.png)

如果只使用蓝色地砖，一共有2种不同的替换方式。

![pe116_3](\images\pe116_3.png)

假定颜色不能混合使用，一共有7 + 3 + 2 = 12种方式替换一行五块黑色地砖。

假定颜色不能混合使用，且至少使用一种彩色地砖，一共有多少种方式替换一行五十块黑色地砖？

注意：这道题与第117题有关。