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%I #14 Feb 18 2018 15:08:21
%S 1,12,36,100,213,408,712,1148,1745,2528,3524,4760,6263,8060,10178,
%T 12644,15485,18728,22400,26528,31139,36260,41918,48140,54953,62384,
%U 70460,79208,88655,98828,109754,121460,133973,147320,161528,176624,192635
%N Number of ways to place 3 nonattacking nightriders on a 3 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="/A172218/b172218.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) = (9n^3 - 57n^2 + 210n - 344)/2, n>=8.
%F G.f.: x*(2*x^10-4*x^9+6*x^8-4*x^7-6*x^6+24*x^5-18*x^4+24*x^3-6*x^2+8*x+1)/(x-1)^4. - _Vaclav Kotesovec_, Mar 25 2010
%t CoefficientList[Series[(2 x^10 - 4 x^9 + 6 x^8 - 4 x^7 - 6 x^6 + 24 x^5 - 18 x^4 + 24 x^3 - 6 x^2 + 8 x + 1) / (x - 1)^4, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 28 2013 *)
%Y Cf. A172141, A061989, A172212.
%K nonn,easy
%O 1,2
%A _Vaclav Kotesovec_, Jan 29 2010
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