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%I #18 Feb 18 2018 15:08:03
%S 1,16,84,412,1126,2760,5739,10982,19695,33068,52801,80638,118731,
%T 169368,235135,318890,423733,553028,710389,899690,1125059,1390880,
%U 1701793,2062694,2478735,2955324,3498125,4113058,4806299,5584280,6453689
%N Number of ways to place 4 nonattacking nightriders on a 4 X n board.
%C A nightrider is a fairy chess piece that can move (proportionate to how a knight moves) in any direction.
%H Vincenzo Librandi, <a href="/A172219/b172219.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) = (32n^4 - 432n^3 + 3190n^2 - 13323n + 25530)/3, n>=18.
%F G.f.: -x * (2*x^21 -6*x^20 +10*x^19 -14*x^18 +22*x^17 -30*x^16 -26*x^15 +162*x^14 -272*x^13 +364*x^12 -466*x^11 +526*x^10 -303*x^9 -207*x^8 +603*x^7 -517*x^6 +489*x^5 -249*x^4 +142*x^3 +14*x^2 +11*x +1) / (x-1)^5. - _Vaclav Kotesovec_, Mar 25 2010
%t CoefficientList[Series[-(2 x^21 - 6 x^20 + 10 x^19 - 14 x^18 + 22 x^17 - 30 x^16 - 26 x^15 + 162 x^14 - 272 x^13 + 364 x^12 - 466 x^11 + 526 x^10 - 303 x^9 - 207 x^8 + 603 x^7 - 517 x^6 + 489 x^5 - 249 x^4 + 142 x^3 + 14 x^2 + 11 x + 1) / (x - 1)^5, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 28 2013 *)
%Y Cf. A061990, A172213, A172218.
%K nonn,easy
%O 1,2
%A _Vaclav Kotesovec_, Jan 29 2010
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