A190394 Maximum number of nonattacking nightriders on an n X n board.

1, 4, 5, 8, 10, 16, 17, 20, 21, 24, 26, 32, 33, 36, 39, 42, 45, 48, 51, 54, 58, 64, 65, 66, 68, 72, 75, 80, 81, 84, 87, 90, 93

Offset: 1

Author

Vaclav Kotesovec, May 10 2011

Keywords

• nonn
• nice
• hard
• more

Comments

A nightrider is a fairy chess piece that can move any distance in a direction specified by a knight move.

Maximum number of nonattacking nightriders on an n X n toroidal board is n.

Examples

			From _Rob Pratt_, Jul 24 2015: (Start)
a(20) = 54:
  XX--XXXX---X------XX
  XX---------X--XX--XX
  --------------------
  ---X----------------
  X-----------------X-
  X-----------------X-
  X-------------------
  X---------X---------
  ------------------XX
  ------------X-------
  -------X------------
  XX------------------
  ---------X---------X
  -------------------X
  -X-----------------X
  -X-----------------X
  ----------------X---
  --------------------
  XX--XX--X---------XX
  XX------X---XXXX--XX
(End)
		

Links

• Andy Huchala, Python program.
• Vaclav Kotesovec, Non-attacking chess pieces, 6ed, 2013, pp. 751-763.
• Rob Pratt, 54 nonattacking nightriders on a 20 X 20 board.

Crossrefs

Cf. A085801, A190393, A172141, A173429.

Formula

2n <= a(n) <= 3n-2, for n > 3.

a(n) >= 24*floor((n+4)/10)-8, for n >= 6. - Vaclav Kotesovec, Apr 01 2012

Extensions

Terms a(11)-a(16) from Vaclav Kotesovec, May 13 2011

Terms a(17)-a(19) from Vaclav Kotesovec, Apr 01 2012

a(20) from Rob Pratt, Jul 24 2015

a(21)-a(32) from Paul Tabatabai, Nov 06 2018

a(33) from Andy Huchala, Mar 30 2024