The OEIS is supported by the many generous donors to the OEIS Foundation.

Number of ways to place 3 nonattacking knights on an n X n toroidal board.
6

%I #14 Feb 20 2018 14:20:53

%S 0,0,6,208,600,3252,10584,27584,61992,125300,233772,409584,682084,

%T 1089172,1678800,2510592,3657584,5208084,7267652,9961200,13435212,

%U 17860084,23432584,30378432,38955000,49454132,62205084

%N Number of ways to place 3 nonattacking knights on an n X n toroidal board.

%H Vincenzo Librandi, <a href="/A172530/b172530.txt">Table of n, a(n) for n = 1..1000</a>

%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens and kings on boards of various sizes</a>

%F a(n) = n^2*(n^4 - 27*n^2 + 218)/6, n>=6.

%F G.f.: -2*x^3 * (50*x^9 -398*x^8 +1425*x^7 -2989*x^6 +3971*x^5 -3325*x^4 +1605*x^3 -365*x^2 +83*x +3) / (x-1)^7. - _Vaclav Kotesovec_, Mar 25 2010

%t CoefficientList[Series[- 2 x^2 (50 x^9 - 398 x^8 + 1425 x^7 - 2989 x^6 + 3971 x^5 - 3325 x^4 + 1605 x^3 - 365 x^2 + 83 x + 3) / (x - 1)^7, {x, 0, 40}], x] (* _Vincenzo Librandi_, May 29 2013 *)

%Y Cf. A172529, A172134, A172518.

%K nonn,easy

%O 1,3

%A _Vaclav Kotesovec_, Feb 06 2010

%E More terms from _Vincenzo Librandi_, May 29 2013

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 20 10:44 EDT 2024. Contains 376068 sequences. (Running on oeis4.)