A379393 Maximum number of connections for a 3 X n rectangle.

1, 6, 72, 277, 1910, 8657, 27442, 97132, 295752, 967914, 2922814

Offset

2,2

Comments

In a 3 X n board (with n > 1) with numbers 1, 2 and 3, at least 2 of each, find the arrangement with more solutions connecting a pair of numbers 1 and a pair of number 2 and a pair of number 3, covering the entire board and without passing through the same square twice.

Terms a(5) and a(7)-a(12) from Giorgio Vecchi.

Links

Table of n, a(n) for n=2..12.

Rodolfo Kurchan and Claudio Meller, Number Connections, Puzzle Fun, Problems (2024).

Example

For n = 2 with the board
  +---+---+
  | 1 | 1 |
  +---+---+
  | 2 | 2 |
  +---+---+
  | 3 | 3 |
  +---+---+
There is only 1 solution being the squares with these letters:
  +---+---+
  | A | B |
  +---+---+
  | C | D |
  +---+---+
  | E | F |
  +---+---+
Solution:
1) AB - CD - EF
There is one solution so a(2) = 1.
.
For n = 3 with the board
  +---+---+---+
  | 1 | 3 | 3 |
  +---+---+---+
  | 1 | 2 | 2 |
  +---+---+---+
  | 1 | 2 | 2 |
  +---+---+---+
the maximum number of solutions is 6 being the squares with this letters:
  +---+---+---+
  | A | B | C |
  +---+---+---+
  | D | E | F |
  +---+---+---+
  | G | H | I |
  +---+---+---+
Solutions:
  1) ADG - BC - HEFI
  2) ADG - BC - FEHI
  3) ADG - BC - EFIH
  4) ADG - BC - EHIF
  5) ADG - BEFC - HI
  6) ADEHG - BC - FI
There are six solutions so a(3) = 6.

Crossrefs

Cf. A379241.

Sequence in context: A338535 A250071 A192990 * A276244 A361571 A282817

Adjacent sequences: A379390 A379391 A379392 * A379394 A379395 A379396

Keyword

nonn,more

Author

Rodolfo Kurchan, Dec 22 2024

Status

approved