A381813 -id:A381813 - cp's OEIS frontend

A381812 Number of moves required to reach a position with the maximum number of heads in the game of blet with 2*n coins.

1, 1, 2, 5, 3, 6, 11, 7, 10, 17, 11, 16, 25, 15, 22, 33, 21, 28, 41, 27, 34

Offset: 2

Pontus von Brömssen, Mar 08 2025

See A075273 or Rodriguez Villegas, Sadun, and Voloch (2002) for the definition of blet.

Rodriguez Villegas, Sadun, and Voloch (2002) prove that the maximum number of heads achievable is A047206(n).

			For n = 5, a(5) = 5 moves are needed to go from HTHTHTHTHT to a sequence with the maximum number A047206(5) = 8 of heads: HTHTHTHTHT -> THHTHTHTHH -> THHTHTTHTH -> THHHTHTHTH -> THHHHTHHTH -> HHHHHTHHHT.

Michael S. Branicky, Python program for OEIS A381812
Fernando Rodriguez Villegas, Lorenzo Sadun, and José Felipe Voloch, Blet: a mathematical puzzle, The American Mathematical Monthly 109 (2002), Issue 8, 729-740.

Cf. A047206, A075273, A381813, A381814.

Python
```
# see linked program
```

a(17)-a(18) from Michael S. Branicky, Mar 11 2025

a(19)-a(22) from Bert Dobbelaere, Mar 15 2025

A381814 Size of the largest component of the blet graph for n coins.

Original entry on oeis.org

2, 5, 20, 8, 56, 56, 74, 180, 660, 220, 2288, 2002, 2942, 7280, 24752, 8568, 93024, 77520, 120920, 298452, 1009470, 346104, 3845600, 3289000, 5067974, 12432420, 42921450, 14307150, 161280600, 140244000, 215188426, 524512560, 1835793960

Offset: 3

Pontus von Brömssen, Mar 08 2025

See A381813 for the definition of the blet graph.

			For n = 4, the blet graph has 2 components of maximum size a(4) = 5: {TTTH, THTT, THHH, HTHT, HHTH} and {TTHT, THTH, HTTT, HTHH, HHHT}.

Michael S. Branicky, Python program for OEIS A381813 and A381814

Cf. A075273, A381812, A381813 (number of components of size at least 2).

Python
```
# see linked program
```

a(2*n) >= A075273(n) (the size of the component containing the vertex (HT)^n).

a(24)-a(28) from Michael S. Branicky, Mar 08 2025
a(29)-a(30) from Michael S. Branicky, Mar 12 2025
a(31)-a(35) from Bert Dobbelaere, Mar 16 2025

cp's OEIS Frontend

A381812 Number of moves required to reach a position with the maximum number of heads in the game of blet with 2*n coins.

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