Object type  
String length $n$  (max. 20) 
Output format  
By ignoring the labeling of the stamps (stamp $i$ is identified with stamp $n+1i$) and the orientation of the pile (we may swap left and right) we obtain unlabeled stamp foldings. A semimeander is a stamp folding in which stamp 1 can be seen from above. A symmetric semimeander is a semimeander in which stamp 2 is left of stamp 1. An open meander is a stamp folding in which stamp 1 can be seen from above left, and stamp $n$ can be seen from above right if $n$ is even and from the bottom (right) if $n$ is odd. Meanders count the number of ways that a river flowing from west to east, starting in the northwest and ending in the northeast if $n$ is even and the southeast if $n$ is odd, crosses a straight line. Symmetric meanders are obtained by considering open meanders modulo eastwest symmetry. The following figure shows all the different variants for $n=4$, where stamp 1 is marked by a little dot, and the gray horizontal line shows the lefttoright order in which we consider the pile of stamps.
permu tations 
stamp foldings 
unlabeled stamp foldings 
semi meanders 
symmetric semi meanders 
open meanders 
symmetric meanders 

1  4321  =16  
2  3421  =15  
3  3214  =12  =12  
4  2431  =13  
5  2341  =12  
6  4213  =13  
7  2143  
8  2134  =15  
9  4312  =15  
10  3412  =7  
11  3124  =13  
12  1432  =5  
13  1342  =4  
14  4123  =12  =3  
15  1243  =2  
16  1234  =1 
The algorithms running on this website are described in Sawada and Li's paper [SL12].
Links to the objects in the Online Encyclopedia of Integer Sequences: