A353259 Solution to Snake Numbers Problems for Snakes from 1 to n for an n X n square grid (see Comments).

1, 4, 7, 16, 19, 36, 39, 64, 67, 100

Offset

1,2

Comments

On an n X n square board we draw a path with squares that we number 1, 2, ..., n, 1, 2, ..., n, 1, ... of the greatest length, which will be a(n). The path advances from one number to the next horizontally or vertically, not diagonally, after n it goes back to number 1. The path cannot cross itself. There cannot be repeated numbers in the same row or column.

Links

Table of n, a(n) for n=1..10.

Rodolfo Kurchan, Puzzle Fun, Snake Number Problem.

Formula

a(n) = n^2 for even n.

Example

a(5) = 19 from Giorgio Vecchi:
  +---+---+---+---+---+
  |  2|  3|  4|  5|  1|
  +---+---+---+---+---+
  |  1|   |   |  3|  2|
  +---+---+---+---+---+
  |   |  1|  5|  4|   |
  +---+---+---+---+---+
  |  3|  2|   |   |  4|
  +---+---+---+---+---+
  |  4|  5|  1|  2|  3|
  +---+---+---+---+---+
.
a(7) = 39 from Giorgio Vecchi.
a(9) = 67 from Giorgio Vecchi.
For odd n >= 3 the solutions up to now have a(n) = (n-1)^2+3.

Crossrefs

Sequence in context: A130665 A236305 A212062 * A345429 A256926 A101534

Adjacent sequences: A353256 A353257 A353258 * A353260 A353261 A353262

Keyword

nonn,more

Author

Rodolfo Kurchan, Apr 08 2022

Status

approved