A371606 Number of ways to fold with complete turns a strip of n blank double-sided sticky stamps.

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).

Links

Table of n, a(n) for n=1..17.

Klemen Klanjscek, Python program for counting sticky unlabeled stamp foldings

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

Adjacent sequences: A371603 A371604 A371605 * A371607 A371608 A371609

Keyword

nonn,more,changed

Author

Klemen Klanjscek, Mar 29 2024

Extensions

a(15)-a(17) from Klemen Klanjscek, Jul 09 2024

Status

approved