OFFSET
1,2
COMMENTS
The king visits the Moore neighborhood (see A272763). The piece does not pay attention to its position and will fall off the board if it makes a move beyond the edge of the board.
LINKS
Hugo Pfoertner, Table of n, a(n) for n = 1..45
Hugo Pfoertner, Plot of A376609(n)/A376610(n) vs n, using Plot 2.
Hugo Pfoertner, Results of a simulation of 10^9 walks on the 8X8 board.
EXAMPLE
1, 8/5, 72/35, 46/19, 23747/8723, 94968/31879, 12161644/3797647, 158536576/46627015, 165181795263/46174521031, ...
Approximately 1, 1.6, 2.057, 2.421, 2.722, 2.979, 3.202, 3.400, 3.577, 3.738, ...
PROG
(PARI) \\ Uses function droprob from A376606
kingmoves = [[1, 0], [0, 1], [0, -1], [-1, 0], [-1, -1], [-1, 1], [1, -1], [1, 1]];
a376609(n) = numerator(droprob(n, kingmoves, 8))
CROSSREFS
A376610 are the corresponding denominators.
KEYWORD
nonn,frac,nice
AUTHOR
Hugo Pfoertner, Oct 03 2024
STATUS
approved