Stamp Folding

The number of ways of folding a strip of stamps has several possible variants. Considering only positions of the hingesfor unlabeled stamps without regard to orientation of the stamps, the number of foldings is denoted . If the stampsare labeled and orientation is taken into account, the number of foldings is denoted . Finally, the number ofsymmetric 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

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.

• Fixed Point Theorem
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