A323749 Triangle read by rows: T(n,m) (1 <= n < m) = number of moves of a (m,n)-leaper (a generalization of a chess knight) until it can no longer move, starting on a board with squares spirally numbered from 1. Each move is to the lowest-numbered unvisited square. T(n,m) = -1 if the path never terminates.

2016, 3723, 4634, 13103, 2016, 1888, 14570, 7574, 1323, 4286, 26967, 3723, 2016, 4634, 1796, 101250, 12217, 4683, 9386, 1811, 3487, 158735, 13103, 5974, 2016, 2758, 1888, 3984, 132688, 33864, 3723, 8900, 6513, 4634, 4505, 7796, 220439, 14570, 36232, 7574, 2016, 1323, 9052, 4286, 5679, 144841, 52738, 19370, 6355, 6425

Offset: 1

Author

Jud McCranie, Jan 26 2019

Keywords

• nonn
• tabf

Comments

The entries are the lower triangle of an array, for an (m,n)-leaper, where 1 <= n < m, ordered: (2,1), (3,1), (3,2), (4,1), (4,2), etc. Are all the paths finite? This appears to be an open question.

Examples

			A chess knight (a (2,1)-leaper) makes 2016 moves before it has no moves available (see A316667). Initial placement on square 1 counts as one move.
		

Links

• Jud McCranie, Table of n, a(n) for n = 1..19900
• N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019).

Crossrefs

Cf. A316667, A323750, A317106, A317471, A317416, A323750, A317438, A317916.

Extensions

Edited by N. J. A. Sloane, Apr 30 2021