A308312 a(n) is the last square visited by knight moves on a spirally numbered (2n-1) X (2n-1) board, moving to the lowest available unvisited square at each step.

1, 1, 14, 30, 69, 108, 150, 205, 264, 333, 408, 475, 553, 659, 763, 881, 1004, 1134, 1274, 1418, 1641, 1811, 1986, 2167, 2358, 2557, 2633, 2978, 2084, 2084, 2084, 2084, 2084, 2084, 2084, 2084, 2084, 2084, 2084, 2084, 2084, 2084, 2084, 2084, 2084, 2084, 2084

Offset

1,3

Comments

A 5 X 5 board, for example, is numbered with the square spiral:

.

21--22--23--24--25

|

20 7---8---9--10

| | |

19 6 1---2 11

| | | |

18 5---4---3 12

| |

17--16--15--14--13

.

a(n) stays constant at 2084 for (2n-1) >= 57 since 2084 is also the last square visited by knight moves on a spirally numbered doubly infinite board, moving to the lowest available unvisited square at each step.

Links

Table of n, a(n) for n=1..47.

Crossrefs

Cf. A316667.

Sequence in context: A083540 A027575 A104776 * A101960 A075208 A228124

Adjacent sequences: A308309 A308310 A308311 * A308313 A308314 A308315

Keyword

nonn

Author

Sangeet Paul, May 19 2019

Status

approved