Map Folding
A general Formula giving the number of distinct ways of folding an 
rectangular map is not known. Adistinct folding is defined as a permutation of 
numbered cells reading from the top down.Lunnon (1971) gives values up to 
.
 |  |  |  |  |  |
| 1 | 1 | 1 | |||
| 2 | 2 | 8 | |||
| 3 | 6 | 60 | 1368 | ||
| 4 | 16 | 1980 | 300608 | ||
| 5 | 59 | 19512 | 18698669 | ||
| 6 | 144 | 15552 |
The limiting ratio of the number of 
strips to the number of strips isgiven by
See also Stamp Folding
References
Gardner, M. ``The Combinatorics of Paper Folding.'' Ch. 7 in Wheels, Life, and Other Mathematical Amusements. New York: W. H. Freeman, 1983. 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. Lunnon, W. F. ``Multi-Dimensional Strip Folding.'' Computer J. 14, 75-79, 1971.