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A376609
a(n) is the numerator of the expected number of random moves of a chess king to reach a position outside an nXn chessboard, starting in one of the corners.
4
1, 8, 72, 46, 23747, 94968, 12161644, 158536576, 165181795263, 1779861954248, 60921563004721184, 136512657826472304, 38548316743830620183051, 581371653539561314, 2630585854108441990301102856, 120104329127347395409698056, 5092493809189909792181005355935991197, 6666722670813237580783418910187983288
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.
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.
A376606 and A376607 are similar for a rook walk with unit steps.
A376736 and A376737 are similar for a chess knight.
Sequence in context: A226163 A338622 A004165 * A032554 A097255 A115693
KEYWORD
nonn,frac,nice
AUTHOR
Hugo Pfoertner, Oct 03 2024
STATUS
approved