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

1,1

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.

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).

Example

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.

Crossrefs

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

Sequence in context: A309918 A189188 A076582 * A323469 A343178 A125491

Adjacent sequences: A323746 A323747 A323748 * A323750 A323751 A323752

Keyword

nonn,tabf

Author

Jud McCranie, Jan 26 2019

Extensions

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

Status

approved