A general formula giving the number of distinct ways of folding an
rectangular map is not known. A distinct folding is defined as a permutation of numbered cells reading from
the top down. Lunnon (1971) gives values up to .
Gardner, M. "The Combinatorics of Paper Folding." Ch. 7 in Wheels,
Life, and Other Mathematical Amusements. New York: W. H. Freeman, pp. 60-73,
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.Sloane, N. J. A. Sequences A000136/M1614,
A001415/M1891, and A001418/M4587
in "The On-Line Encyclopedia of Integer Sequences."Wells,
M. B. Elements
of Combinatorial Computing. Oxford, England: Pergamon Press, p. 238,
1971.
rectangular map is not known. A distinct folding is defined as a permutation of 
numbered cells reading from
the top down. Lunnon (1971) gives values up to 
.
, 
, ...
sheet of maps is given for 
, 2, ..., etc. by 1, 8, 1368, 300608, 186086600, ... (Lunnon
1971; OEIS A001418).
strips to the number of 
strips is given by
![lim_(n->infty)([1×(n+1)])/([1×n]) in [3.3868,3.9821].](/images/equations/MapFolding/NumberedEquation1.svg)
