login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Maximum number of nonattacking nightriders on an n X n board.
3

%I #47 Apr 02 2024 03:46:50

%S 1,4,5,8,10,16,17,20,21,24,26,32,33,36,39,42,45,48,51,54,58,64,65,66,

%T 68,72,75,80,81,84,87,90,93

%N Maximum number of nonattacking nightriders on an n X n board.

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

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

%H Andy Huchala, <a href="/A190394/a190394.py.txt">Python program</a>.

%H Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, pp. 751-763.

%H Rob Pratt, <a href="/A190394/a190394.pdf">54 nonattacking nightriders on a 20 X 20 board</a>.

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

%F a(n) >= 24*floor((n+4)/10)-8, for n >= 6. - _Vaclav Kotesovec_, Apr 01 2012

%e From _Rob Pratt_, Jul 24 2015: (Start)

%e a(20) = 54:

%e XX--XXXX---X------XX

%e XX---------X--XX--XX

%e --------------------

%e ---X----------------

%e X-----------------X-

%e X-----------------X-

%e X-------------------

%e X---------X---------

%e ------------------XX

%e ------------X-------

%e -------X------------

%e XX------------------

%e ---------X---------X

%e -------------------X

%e -X-----------------X

%e -X-----------------X

%e ----------------X---

%e --------------------

%e XX--XX--X---------XX

%e XX------X---XXXX--XX

%e (End)

%Y Cf. A085801, A190393, A172141, A173429.

%K nonn,nice,hard,more

%O 1,2

%A _Vaclav Kotesovec_, May 10 2011

%E Terms a(11)-a(16) from _Vaclav Kotesovec_, May 13 2011

%E Terms a(17)-a(19) from _Vaclav Kotesovec_, Apr 01 2012

%E a(20) from _Rob Pratt_, Jul 24 2015

%E a(21)-a(32) from _Paul Tabatabai_, Nov 06 2018

%E a(33) from _Andy Huchala_, Mar 30 2024