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%I #10 Dec 18 2015 18:17:43
%S 0,0,0,0,12,82,330,1008,2566,5742,11652,21926,38802,65322,105428,
%T 164214,248022,364764,523998,737334,1018488,1383768,1852104,2445628,
%U 3189660,4113396,5249848,6636636,8315880,10335110,12747090,15610860,18991490
%N Number of ways to arrange 3 nonattacking queens on the lower triangle of an n X n board
%C Column 3 of A194498
%H R. H. Hardin, <a href="/A194493/b194493.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 3*a(n-1) -7*a(n-3) +3*a(n-4) +6*a(n-5) -6*a(n-7) -3*a(n-8) +7*a(n-9) -3*a(n-11) +a(n-12), [_R. H. Hardin_ Aug 26 2011]
%F G.f.: -2*x^5*(18*x^5 + 40*x^4 + 51*x^3 + 42*x^2 + 23*x + 6)/((x-1)^7*(x+1)^3*(x^2+x+1))
%F Explicit formula: n^6/48 - 11*n^5/48 + 15*n^4/16 - 241*n^3/144 + 17*n^2/16 - 17*n/144 + (n^2/8 - 9*n/8 + 17/8)*floor(n/2) + 2/3*floor(n/3), [_Vaclav Kotesovec_, Apr 08 2012]
%e Some solutions for 5X5
%e ..0..........0..........0..........0..........0..........0..........1
%e ..1.0........0.1........1.0........0.0........1.0........0.1........0.0
%e ..0.0.0......0.0.0......0.0.0......1.0.0......0.0.1......0.0.0......0.1.0
%e ..0.1.0.0....1.0.0.0....0.0.0.1....0.0.0.1....0.0.0.0....1.0.0.0....0.0.0.0
%e ..0.0.0.0.1..0.0.1.0.0..0.1.0.0.0..0.1.0.0.0..0.1.0.0.0..0.0.0.1.0..0.0.1.0.0
%K nonn
%O 1,5
%A _R. H. Hardin_ Aug 26 2011
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