|String length $n$||(max. 20)|
By ignoring the labeling of the stamps (stamp $i$ is identified with stamp $n+1-i$) and the orientation of the pile (we may swap left and right) we obtain unlabeled stamp foldings. A semi-meander is a stamp folding in which stamp 1 can be seen from above. A symmetric semi-meander is a semi-meander 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 north-west and ending in the north-east if $n$ is even and the south-east if $n$ is odd, crosses a straight line. Symmetric meanders are obtained by considering open meanders modulo east-west 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 left-to-right order in which we consider the pile of stamps.
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: