Somewhere between counting labeled stamp foldings and unlabeled stamp foldings, consider folding strips of stamps with alternating colors.
Two stamps, two distinct foldings:
Three stamps, three foldings:
Four stamps, six foldings:
Five stamps, 10 foldings:
Six stamps, 20 foldings:
Seven stamps, 35 foldings:
If you kind of liked this, you’ll kind of love map foldings, labeled stamp foldings, unlabeled stamp foldings, symmetric stamp foldings, or symmetric unlabeled stamp foldings.
See Martin Gardner, Wheels, Life and Other Mathematical Amusements, pp. 60–61, 1983.
Figures created with Wolfram Mathematica versions 11 and 15.
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