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

3,1

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.

Links

Table of n, a(n) for n=3..35.

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

Example

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}.

Prog

(Python) # see linked program

Crossrefs

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

Sequence in context: A259879 A016556 A067050 * A394713 A001355 A385600

Adjacent sequences: A381810 A381811 A381812 * A381814 A381815 A381816

Keyword

nonn,more

Author

Pontus von Brömssen, Mar 08 2025

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

Status

approved