A368657 Number of cycles in an n X n grid where the cycle cannot touch itself orthogonally or diagonally and must contain at least one inside point.

0, 0, 1, 13, 167, 2685, 50391, 1188935, 41749885, 2645126227, 341643017303, 82472721488013, 31312529515504513, 17381378412860375479, 14419291783372365769995, 18997663191047558313462721

Offset: 1

Author

Niklas Gustavsson, Jan 02 2024

Keywords

• nonn
• more

Comments

For n > 1, n < 5, this shares the sequence with n-1 in A140517. Cycles are not reduced by symmetry (rotation, translation or mirroring). The grid can only have one cycle.

Examples

			For n = 4, there are 13 valid cycles:
.
  1      2      3      4
  ###.   .###   ....   ....
  #.#.   .#.#   .###   ###.
  ###.   .###   .#.#   #.#.
  ....   ....   .###   ###.
.
  5      6      7     8
  ####   ....   ###.  .###
  #..#   ####   #.#.  .#.#
  ####   #..#   #.#.  .#.#
  ....   ####   ###.  .###
.
  9      10     11    12
  .###   ###.   ####  ####
  ##.#   #.##   #..#  #..#
  #..#   #..#   #.##  ##.#
  ####   ####   ###.  .###
.
  13
  ####
  #..#
  #..#
  ####
		

Links

• Cracking The Cryptic, The Trouble With Circular Reasoning Is.... (!), YouTube.
• Jimmy Mårdell, Python code used for generation of the sequence.

Crossrefs

Cf. A140517, A297664.