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

Author

Sangeet Paul, May 19 2019

Keywords

• nonn

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.

Crossrefs

Cf. A316667.