A375925 Squares visited by a king moving on a walled, spirally numbered board, where a wall must be jumped on each move, always to the lowest available unvisited square.

1, 4, 14, 3, 11, 2, 8, 22, 7, 19, 5, 15, 33, 13, 29, 12, 28, 10, 24, 9, 23, 45, 21, 41, 20, 6, 18, 38, 17, 35, 16, 34, 60, 32, 58, 31, 55, 30, 54, 86, 52, 26, 48, 25, 47, 77, 46, 76, 44, 74, 43, 71, 42, 70, 40, 68, 39, 67, 37, 63, 36, 62, 96, 61, 95, 59, 93

Offset

1,2

Comments

Board is numbered with the walled, square spiral:

.

17 16 15 14 13 | .

------------- | .

18 | 5 4 3 |12 | .

| ----- | | .

19 | 6 | 1 2 |11 | .

| --------- | .

20 | 7 8 9 10 | .

----------------- .

21 22 23 24 25 26

.

Walls mark off the path of the spiral.

A king move must go through a wall when drawing a line between the center of the start and end square. Note that some moves touch a wall but do not pass through a wall (e.g. 1 to 3), these are not permissible.

Due to the wall rule, the next term cannot be +/-1 or +/-2.

Links

Sameer Khan, Table of n, a(n) for n = 1..100

Kevin Ryde, Path Plot

Example

For n = 2, a(n) = 4 because moving to 2 or 3 does not pass through a wall.

Crossrefs

Cf. A033638, A316667 (trapped knight), A336038 (trapped king).

Sequence in context: A107775 A003117 A239465 * A156985 A138229 A131702

Adjacent sequences: A375922 A375923 A375924 * A375926 A375927 A375928

Keyword

nonn

Author

Sameer Khan, Sep 03 2024

Status

approved