

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 lowestnumbered unvisited square. T(n,m) = 1 if the path never terminates.


4



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
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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



