cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

5, 8, 37, 176, 196, 1471, 6885, 5948, 60460, 280600, 199316, 2533987, 11698223, 7080928, 107594213, 494889092, 261542752
Offset: 2

Views

Author

N. J. A. Sloane, Oct 12 2002

Keywords

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

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

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

Original entry on oeis.org

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

Views

Author

Pontus von Brömssen, Mar 08 2025

Keywords

Comments

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).

Examples

			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.

Links

Crossrefs

Cf. A047206, A075273, A381813, A381814.

Programs

  • Python
    # see linked program

Extensions

a(17)-a(18) from Michael S. Branicky, Mar 11 2025
a(19)-a(22) from Bert Dobbelaere, Mar 15 2025

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

Original entry on oeis.org

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

Views

Author

Pontus von Brömssen, Mar 08 2025

Keywords

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

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
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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