%I #19 Aug 22 2024 14:31:07
%S 0,0,29,661,6285,35378,143787,468529,1301351,3202970,7170593,14872997,
%T 28969129,53527866,94568255,160741233,264175507,421511954,655152581,
%U 994751765,1478979173,2157585442,3093803379,4367119121,6076449375,8343762538,11318183177
%N Number of ways to place 4 non-attacking ferses on an n X n board.
%C Fers is a leaper [1,1].
%H Vincenzo Librandi, <a href="/A201245/b201245.txt">Table of n, a(n) for n = 1..1000</a>
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, p.415
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
%F a(n) = (n^8 - 30n^6 + 48n^5 + 299n^4 - 912n^3 - 462n^2 + 4368n - 4200)/24, n>=3.
%F G.f.: -x^3*(2*x^8 - 55*x^7 + 230*x^6 - 254*x^5 - 225*x^4 + 173*x^3 + 1380*x^2 + 400*x + 29)/(x-1)^9.
%t CoefficientList[Series[- x^2 (2 x^8 - 55 x^7 + 230 x^6 - 254 x^5 - 225 x^4 + 173 x^3 + 1380 x^2 + 400 x + 29)/(x-1)^9, {x, 0, 40}], x] (* _Vincenzo Librandi_, Apr 30 2013 *)
%Y Cf. A172127, A201243, A201244, A201246, A201247, A201248.
%K nonn,easy
%O 1,3
%A _Vaclav Kotesovec_, Nov 28 2011