A379241 Maximum number of connections for a 2 X n rectangle.

1, 5, 22, 54, 134, 269, 534, 934, 1618, 2573, 4062, 6030, 8902, 12549, 17614, 23854, 32194, 42229, 55238

Offset

2,2

Comments

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

Terms a(7)-a(20) from Giorgio Vecchi.

In a vertex-colored graph, partition the vertices into paths of positive lengths. It is required that the two terminal vertices of each path have the same color, and that there is exactly one such path for each color of the terminal vertices. a(n) is the maximum number of such partitions for all possible 2-colorings (at least two vertices of each color) of the 2 X n grid graph. - Pontus von Brömssen, Dec 19 2024

Links

Table of n, a(n) for n=2..20.

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

Example

For n = 3 the with the board
  +---+---+---+
  | 1 | 1 | 2 |
  +---+---+---+
  | 1 | 2 | 2 |
  +---+---+---+
the maximum number of solutions is 5 being the squares with this letters:
  +---+---+---+
  | A | B | C |
  +---+---+---+
  | D | E | F |
  +---+---+---+
Solutions:
  1) ABED - CF
  2) ADEB - CF
  3) BAD - CFE
  4) AD - CBEF
  5) AD - EBCF
There are five solutions so a(3) = 5.

Crossrefs

Sequence in context: A273075 A272824 A373110 * A273677 A209116 A301499

Adjacent sequences: A379238 A379239 A379240 * A379242 A379243 A379244

Keyword

nonn,more

Author

Rodolfo Kurchan, Dec 18 2024

Status

approved