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%I #9 Sep 12 2015 11:00:23
%S 0,0,0,0,0,0,0,12,60,180,432,900,1692,2940,4800,7452,11100,15972,
%T 22320,30420,40572,53100,68352,86700,108540,134292,164400,199332,
%U 239580,285660,338112,397500,464412,539460,623280,716532,819900,934092,1059840
%N Number of ways to place 4 nonattacking amazons (superqueens) on a 4 X n board.
%C An amazon (superqueen) moves like a queen and a knight
%H Vincenzo Librandi, <a href="/A174642/b174642.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="http://oprisch.net/SuperQueens/SuperQueens.html">The Oprisch Family Web Site</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 G.f.: -12*x^8*(x^3+1)/(x-1)^5.
%F Explicit formula: a(n) = (n-7)(n^3-21n^2+158n-420), n>=7.
%t CoefficientList[Series[- 12 x^7 (x^3 + 1) / (x - 1)^5, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 30 2013 *)
%Y Cf. A173214, A172201, A172200, A051223, A051224, A036464.
%K nonn,easy
%O 1,8
%A _Vaclav Kotesovec_, Mar 25 2010
%E More terms from _Vincenzo Librandi_, May 30 2013
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