Map folding is the problem of counting distinct ways to fold an rectangular map into a stack one cell wide. A distinct
folding is defined by the permutation of its numbered cells read from the top
down. A general formula for the count is not known. Lunnon
(1971) tabulates strip counts through .
The number of ways to fold an map is given for , 2, ... by 1, 8, 1368, 300608, 186086600, ... (Lunnon 1971;
OEIS A001418).
Let count the foldings of a strip. The growth rate
exists (Legendre 2014). Gardner (1983) reports the bounds from unpublished work of Lunnon.
Convergence of the successive ratio to follows under the conjectured asymptotic
form (Legendre 2014).
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.Legendre, S. "Foldings
and Meanders." Austral. J. Combin.58, 275-291, 2014. https://ajc.maths.uq.edu.au/pdf/58/ajc_v58_p275.pdf.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 into a stack one cell wide. A distinct
folding is defined by the permutation of its 
numbered cells read from the top
down. A general formula for the count is not known. Lunnon
(1971) tabulates strip counts through 
.
, 
, ...
map is given for 
, 2, ... by 1, 8, 1368, 300608, 186086600, ... (Lunnon 1971;
OEIS A001418).
count the foldings of a 
strip. The growth rate
from unpublished work of Lunnon.
Convergence of the successive ratio 
to 
follows under the conjectured asymptotic
form 
(Legendre 2014).
