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

Author

Rodolfo Kurchan, Apr 08 2022

Keywords

• nonn
• more

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.

Examples

			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.
		

Links

• Rodolfo Kurchan, Puzzle Fun, Snake Number Problem.

Formula

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