The number of ways of folding a strip of stamps has several possible variants. Considering only positions of the hinges for unlabeled stamps without regard to orientation of the stamps, the number of foldings is denoted . If the stamps are labeled and orientation is taken into account, the number of foldings is denoted . Finally, the number of symmetric foldings is denoted . The following table summarizes these values for the first .
Sloane | Sloane's A001010 | Sloane's A001011 | Sloane's A000136 |
1 | 1 | 1 | 1 |
2 | 2 | 1 | 2 |
3 | 2 | 2 | 6 |
4 | 4 | 5 | 16 |
5 | 6 | 14 | 50 |
6 | 8 | 38 | 144 |
7 | 18 | 120 | 462 |
8 | 20 | 353 | 1392 |
9 | 56 | 1148 | 4536 |
10 | 48 | 3527 | 14060 |
See also Map Folding
References
Gardner, M. ``The Combinatorics of Paper-Folding.'' In Wheels, Life, and Other Mathematical Amusements. New York: W. H. Freeman, pp. 60-73, 1983.
Ruskey, F. ``Information of Stamp Folding.''
http://sue.csc.uvic.ca/~cos/inf/perm/StampFolding.html.
Sloane, N. J. A. A Handbook of Integer Sequences. Boston, MA: Academic Press, p. 22, 1973.