A035289 - OEIS

%I #16 Sep 08 2022 08:44:52

%S 0,12,56,192,504,1100,2112,3696,6032,9324,13800,19712,27336,36972,

%T 48944,63600,81312,102476,127512,156864,191000,230412,275616,327152,

%U 385584,451500,525512,608256,700392,802604,915600,1040112,1176896

%N Number of ways to place a non-attacking white and black knight on n X n chessboard.

%H Vincenzo Librandi, <a href="/A035289/b035289.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = n^4 - 9 n^2 + 24 n - 16.

%F G.f.: 4*x^2*(4*x^3-8*x^2+x-3)/(x-1)^5. [_Colin Barker_, Jan 09 2013]

%e There are 56 ways of putting 2 distinct knights on 3 X 3 so that neither can capture the other

%t CoefficientList[Series[4 x (4 x^3 - 8 x^2 + x - 3)/(x - 1)^5, {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 20 2013 *)

%o (Magma) [n^4 - 9*n^2 + 24*n - 16: n in [1..50]]; // _Vincenzo Librandi_, Oct 20 2013

%K nonn,easy

%O 1,2

%A _Erich Friedman_