5293: Cannon

ZYT found a chessboard with two rows and $x$

In Chinese Chess, if a cannon and another piece (let’s call it A) are in the same row or column, and there is exactly one other piece in between, this cannon can capture A and move to A's original position.(In this problem, in order to keep the situation simple, we think that a cannon can capture any piece except itself, without considering which side it belongs to. ) 

Now, ZYT has performed a series of operations on these cannons. Define an operation (l_i,a_i,b_i)(l_i,a_i,b_i) as the aithaith cannon currently counting from left to right in the lithlith row has eaten the bithbith cannon of the same row, where 1≤a_i,b_i≤c,∣a_i−b_i∣=2,l∈{1,2}1≤a_i,b_i≤c,∣a_i−b_i∣=2,l∈{1,2}(cc is the number of cannons in this row). Define an operation sequence as an ordered arrangement of a series of operations. 

ZYT wants to get many different sequences of operations. He is bored, so he wants to know how many different operation sequences can be generated for $i$

Specifically, he wants to know how many different operation sequences can be generated for i times under the following two rules: 

1. ZYT can perform any operation that meets the above rules. 
2. In all operations performed by ZYT, there are no two integers p,q, satisfying 1≤p<q≤i and l_p>l_q.