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

Author

N. J. A. Sloane, Oct 12 2002

Keywords

• nonn
• more

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

Examples

			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
		

Links

• 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.

Crossrefs

Cf. A075274, A381814.

Programs

Python

# see linked program

Formula

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

Extensions

Offset corrected by Michel Marcus, Sep 30 2017

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