A075273 Number of reachable arrangements of coins in the game Blet starting with 2n coins.

5, 8, 37, 176, 196, 1471, 6885, 5948, 60460, 280600, 199316, 2533987, 11698223, 7080928, 107594213, 494889092, 261542752

Offset

2,1

Comments

In Blet with 2n coins, we start with 2n coins alternating heads and tails, (HT)^n, in a circle. A move in Blet is either of transitions HTH -> THT or THT -> HTH. This sequence counts the number of arrangements of coins that can be reached by applying these transitions an arbitrary number of times. - Sean A. Irvine, Feb 14 2025

Links

Table of n, a(n) for n=2..18.

Michael S. Branicky, Python program for OEIS A075273

Sean A. Irvine, Java program (github)

F. Rodriguez Villegas, L. Sadun, and J. F. Voloch, Blet: a mathematical puzzle, Amer. Math. Monthly, 109 No.8 (2002), 729-740.

Formula

a(n) <= A381814(2*n). - Pontus von Brömssen, Mar 08 2025

Example

For 4 coins, starting from HTHT we can reach THTT, HHTH, TTTH, THHH, and no others, hence a(2) = 5. - Sean A. Irvine, Feb 14 2025

Prog

(Python) # see linked program

Crossrefs

Cf. A075274, A381814.

Sequence in context: A188065 A204676 A219947 * A176859 A176757 A280965

Adjacent sequences: A075270 A075271 A075272 * A075274 A075275 A075276

Keyword

nonn,more

Author

N. J. A. Sloane, Oct 12 2002

Extensions

Offset corrected by Michel Marcus, Sep 30 2017

a(16)-a(18) from and name clarified by Sean A. Irvine, Feb 14 2025

Status

approved