A172964 - OEIS

%I #12 Feb 20 2018 14:19:38

%S 0,4,18,92,230,522,1022,1808,2970,4610,6842,9792,13598,18410,24390,

%T 31712,40562,51138,63650,78320,95382,115082,137678,163440,192650,

%U 225602,262602,303968,350030,401130,457622,519872,588258,663170,745010,834192,931142,1036298,1150110

%N Number of ways to place 2 nonattacking knights on an n X n cylindrical board.

%H Vincenzo Librandi, <a href="/A172964/b172964.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*(n^3 - 9*n + 12)/2, n>=5.

%F G.f.: 2*x^2*(6*x^7-30*x^6+61*x^5-66*x^4+45*x^3-21*x^2+x-2)/(x-1)^5. - _Vaclav Kotesovec_, Mar 25 2010

%t CoefficientList[Series[2 x (6 x^7 - 30 x^6 + 61 x^5 - 66 x^4 + 45 * x^3 - 21 x^2 + x - 2) / (x - 1)^5, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 29 2013 *)

%Y Cf. A172529, A172132.

%K nonn,easy

%O 1,2

%A _Vaclav Kotesovec_, Feb 06 2010

%E More terms from _Vincenzo Librandi_, May 29 2013