A Google interview question

The problem is as follows:
The numbers below are arranged according to certain rules. Which numbers should be entered in the last row?
1
11
1121
122111
?

(The following answers are taken from the Internet)

The appearance series is the series that generates the next column according to the appearance. The first column is "1", the second column describes the first column "1" and the second column is "11 」, the third column describes the second column "2 1" and "21", and the fourth column "1211. Change and explore the original description from left to right and the sequence that generates the next series, and then find out whether there are rules. Another part of the study is to explore changing the starting value of the sequence and find out the rule from it.

A. Motivation:
Because the course at the second stage is an equal difference series, after the course is completed, we start to have a great interest in the series. We asked the teacher questions.
Later, the teacher gave us another more challenging series-appearance series. We studied it further and happened to have encountered a mathematical science exhibition, so we decided to use it as the topic.
B. Purpose:
In order to find out the pattern of the appearance series, that is, to develop different types of series, we will start to discuss and study and hope to further understand the type of the appearance series. Unveil the world of series!

C. Research equipment and equipment:
Paper and pen, four stinks of knowledge.
D. study process and method:
I. How to use this series is as follows:
1. basic rule: "appearance series" is the series of the next column based on appearance. The first column is "1", the second column describes the first column "1" and the second column is "11 」, the third column describes the second column "2 1" and "21", and the fourth column "1211.
Take "13112221" as an example. Read "one 1, one 3, two 1, and three 2" from the left and right.
, A 1, so the next series is written as "1113213211" from left to right 」.
2. sequence change rules: four methods are available: left-to-left, left-to-right, right-to-right, and right-to-left, which are defined: examples of the reading order and writing order are as follows:
Left-hand: the next column of "13112221" is "1113213211 」.
Left and right: the next column of "13112221" is "1123123111 」.
Right-read: the next column of "13112221" is "1131122311 」
Right-click it and write it to the left. The next column of "13112221" is "1132211311 」
3. Change the starting value of the sequence:
For example:
The start value is the same: 1, 11, 111221, and.
Different start values: 3, 13, 132113, 31
A, 1a, 111a, 311a, 13211a
E. Study Results:
(1) Basic Nature
(1) The appearance sequence is composed of 1, 2, 3, which can be 111 (three 1) or 222 (three 2) at most. No 333 or 4 occurs.
(2) The proportions of 1, 2, and 3 in each column tend to be fixed. 1 accounts for 50%, 2 accounts for 31%, and 3 accounts for 19%.
Left to left:
13112221
Left-side Navigation Pane:
212221221
Right: left:
2112111331
Write Right
12221131
(2) Repeatability
(1) first-end alignment. The first end of every three columns is the same and has three cycles of repeatability.
(2) tail end alignment. The tail ends of every four columns are the same and have four cycles of repetition.
(3) The repetitive content at the beginning and end increases with the increase of the number of columns.
(3) Appearance Series
Research methods focus on four types
~ Left to left> from the left and in sequence, write numbers from left to right. For example: 13: 1113 (1, 1, 3)
~ Read from left to right> read from left but write from right to left, EX: 13 write 3111 (read from left to right, write from right to left, 1 3, 1)
~ Right-looking left-writing> from the right-side view, but write from left to right in sequence. Write 1311 (write from right to left, write from left to right, 1 3, 1)
~ Right: Write> On the right: Write a series from right to left: Write 1131 (read from right to left, write from right to left, 1 for 3, 1 for 1)

F. Conclusions and applications:
Later we found that this appearance series does not correspond to an algebra. His law is more complex than we thought, and it is more challenging to study it. The numbers of the same type must be summarized and described together. Therefore, it is not possible to obtain a complex series. In addition, we also need to find out his rule from four aspects. In the process, we used his "repetition" To Quickly arrange the series.