%I #20 Sep 12 2015 11:00:23
%S 0,0,0,0,0,0,588,3328,9720,27600,59048,124992,226460,408464,666900,
%T 1086464,1650768,2505168,3610000,5198400,7191828,9945232,13320220,
%U 17835264,23265000,30341584,38718648,49401408,61880780,77504400,95550308,117788672,143225280,174144464,209210400,251325504,298732228,355068048,418062060,492217600
%N Number of ways to place 3 nonattacking amazons (superqueens) on an n X n toroidal board.
%C An amazon (superqueen) moves like a queen and a knight.
%H Vincenzo Librandi, <a href="/A178973/b178973.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, 2013
%F a(n) = 1/3*n^2*(n^4/2 -6*n^3 +61*n^2/4 +42*n -285/2 +(3*n^2/4 -6*n +21/2)*(-1)^n), n>=7.
%F G.f.: -4*x^7 * (36*x^11 -47*x^10 -178*x^9 +228*x^8 +354*x^7 -419*x^6 -356*x^5 +297*x^4 +182*x^3 +178*x^2 +538*x +147)/((x-1)^7*(x+1)^5).
%t CoefficientList[Series[- 4 x^6 (36 x^11 - 47 x^10 - 178 x^9 + 228 x^8 + 354 x^7 - 419 x^6 - 356 x^5 + 297 x^4 + 182 x^3 + 178 x^2 + 538 x + 147) / ((x - 1)^7 (x + 1)^5), {x, 0, 50}], x] (* _Vincenzo Librandi_, May 31 2013 *)
%Y Cf. A172201, A172518, A178972.
%K nonn,easy
%O 1,7
%A _Vaclav Kotesovec_, Jan 02 2011
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