info prev up next book cdrom email home

Stamp Folding

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 $U(n)$. If the stamps are labeled and orientation is taken into account, the number of foldings is denoted $N(n)$. Finally, the number of symmetric foldings is denoted $S(n)$. The following table summarizes these values for the first $n$.

$n$ $S(n)$ $U(n)$ $N(n)$
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.




© 1996-9 Eric W. Weisstein
1999-05-26