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# 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 . 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 A001010 A001011 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

Map Folding, Postage Stamp Problem

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## References

Gardner, M. "The Combinatorics of Paper-Folding." In Wheels, Life, and Other Mathematical Amusements. New York: W. H. Freeman, pp. 60-73, 1983.Gardner, M. The Sixth Book of Mathematical Games from Scientific American. Chicago, IL: University of Chicago Press, pp. 21 and 26-27, 1984.Koehler, J. E. "Folding a Strip of Stamps." J. Combin. Th. 5, 135-152, 1968.Lunnon, W. F. "A Map-Folding Problem." Math. Comput. 22, 193-199, 1968.Ruskey, F. "Information of Stamp Folding." http://www.theory.csc.uvic.ca/~cos/inf/perm/StampFolding.html.Sloane, N. J. A. A Handbook of Integer Sequences. Boston, MA: Academic Press, p. 22, 1973.Sloane, N. J. A. Sequences A000136/M1614, A001010/M0323, and A001011/M1455 in "The On-Line Encyclopedia of Integer Sequences."

Stamp Folding

## Cite this as:

Weisstein, Eric W. "Stamp Folding." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StampFolding.html