A381813 Number of connected components, not counting isolated vertices, of the blet graph for n coins.

3, 2, 1, 7, 2, 5, 8, 8, 6, 50, 12, 30, 61, 62, 47, 417, 102, 303, 682, 696, 532, 4904, 1250, 3854, 8911, 9218, 7147, 66735, 17298, 53965, 126348, 131740, 103080

Offset: 3

Author

Pontus von Brömssen, Mar 08 2025

Keywords

• nonn
• more

Comments

The blet graph for n coins has one vertex for each binary heads/tails-sequence of length n. Two vertices are connected by an edge if there is a legal move between them in the game of blet, i.e., if one can be obtained from the other by replacing one occurrence of a triple THT with HTH. The binary sequences are circularly connected, so such a triple is allowed to start at one of the last two elements of the sequence and continue from the beginning.

The number of isolated vertices is A007039(n).

A075273(n) is the size of the component containing (HT)^n in the blet graph for 2*n coins.

Examples

			For n = 4, the blet graph has A007039(4) = 6 isolated vertices TTTT, TTHH, THHT, HTTH, HHTT, HHHH, and a(4) = 2 components of size at least 2: {TTTH, THTT, THHH, HTHT, HHTH} and {TTHT, THTH, HTTT, HTHH, HHHT}.
		

Links

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

Crossrefs

Cf. A007039, A075273, A381812, A381814 (size of the largest component).

Programs

Python

# see linked program

Extensions

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