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A371606
Number of ways to fold with complete turns a strip of n blank double-sided sticky stamps.
0
1, 1, 2, 5, 14, 38, 116, 337, 1024, 3022, 9068, 26736, 79165, 231933, 679344, 1976199, 5738101
OFFSET
1,3
COMMENTS
The unlabeled sticky stamps have glue on both sides. Once two stamps are glued they cannot be separated. When constructing a folding we are not allowed to make partial folds (turns less than 180 degrees).
First 6 terms agree with the sequence A001011, afterwards a(n) < A001011(n).
EXAMPLE
For n = 7 foldings (1 6 5 4 3 2 7), (4 5 6 1 7 2 3), (3 4 5 6 1 7 2), and (1 7 2 3 4 5 6) cannot be produced if stamps are sticky on both sides and we are only allowed to do complete folds. If stamps are not sticky and we are still only allowed to do complete folds, these foldings are still possible. For example, folding strategy for (1 6 5 4 3 2 7):
Unfolded:
<1--2--3--4--5--6--7>
Step 1:
/-3--4--5--6--7>
\-2--1>
Step 2:
<7--6--5--4-\
/-3-/
\-2--1>
Step 3:
<7--6-\
/-5-/
\-4-\
/-3-/
\-2--1>
Step 4:
/---6-\
| /-5-/
| \-4-\
| /-3-/
| \-2--1>
\---7>
Step 5:
<1---\
/---6-\ |
| /-5-/ |
| \-4-\ |
| /-3-/ |
| \-2---/
\---7>
If stamps are sticky, this strategy fails, because after the first step stamps 1 and 4 cannot be separated (every other strategy also fails).
PROG
(Python) # See Link
CROSSREFS
Cf. A001011.
Sequence in context: A006574 A053419 A079227 * A148314 A001011 A148315
KEYWORD
nonn,more
AUTHOR
Klemen Klanjscek, Mar 29 2024
EXTENSIONS
a(15)-a(17) from Klemen Klanjscek, Jul 09 2024
STATUS
approved