A323749 Triangle read by rows: T(m,n) (1 <= n < m) is the number of moves of an (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(m,n) = -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

2,1

Comments

Are all the paths finite? This appears to be an open question.

Links

Jud McCranie, Table of n, a(n) for n = 2..19901

N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019).

Example

Triangle begins:
  m\n|      1     2     3    4    5    6    7    8    9
  ---+-------------------------------------------------
   2 |   2016
   3 |   3723  4634
   4 |  13103  2016  1888
   5 |  14570  7574  1323 4286
   6 |  26967  3723  2016 4634 1796
   7 | 101250 12217  4683 9386 1811 3487
   8 | 158735 13103  5974 2016 2758 1888 3984
   9 | 132688 33864  3723 8900 6513 4634 4505 7796
  10 | 220439 14570 36232 7574 2016 1323 9052 4286 5679
  ...
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. A306197, A323469 (first column), A323750, A343178 (main diagonal).

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

Sequence in context: A309918 A189188 A076582 * A323469 A343178 A125491

Adjacent sequences: A323746 A323747 A323748 * A323750 A323751 A323752

Keyword

nonn,tabl

Author

Jud McCranie, Jan 26 2019

Extensions

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

Offset changed by Pontus von Brömssen, Dec 15 2025

Status

approved