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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, 0, 1, 13, 167, 2685, 50391, 1188935, 41749885, 2645126227, 341643017303, 82472721488013, 31312529515504513, 17381378412860375479, 14419291783372365769995, 18997663191047558313462721
OFFSET
1,4
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.
EXAMPLE
For n = 4, there are 13 valid cycles:
.
1 2 3 4
###. .### .... ....
#.#. .#.# .### ###.
###. .### .#.# #.#.
.... .... .### ###.
.
5 6 7 8
#### .... ###. .###
#..# #### #.#. .#.#
#### #..# #.#. .#.#
.... #### ###. .###
.
9 10 11 12
.### ###. #### ####
##.# #.## #..# #..#
#..# #..# #.## ##.#
#### #### ###. .###
.
13
####
#..#
#..#
####
CROSSREFS
Sequence in context: A012828 A119539 A277412 * A171318 A078362 A157381
KEYWORD
nonn,more
AUTHOR
Niklas Gustavsson, Jan 02 2024
STATUS
approved