%I #6 Dec 18 2015 18:17:43

%S 0,0,0,1,230,4257,44005,312296,1693828,7449231,27785786,90732814,

%T 265594944,709634275,1755164932,4063548824,8885486966,18484419808,

%U 36802865115,70481362597,130377759323,233782433461,407584477894

%N Number of ways to arrange 6 nonattacking knights on the lower triangle of an n X n board

%C Column 6 of A194492

%H R. H. Hardin, <a href="/A194490/b194490.txt">Table of n, a(n) for n = 1..42</a>

%F Empirical: a(n) = (1/46080)*n^12 + (1/7680)*n^11 - (17/3072)*n^10 - (13/4608)*n^9 + (6635/9216)*n^8 - (66667/23040)*n^7 - (2096789/46080)*n^6 + (1744105/4608)*n^5 + (10251671/11520)*n^4 - (107575289/5760)*n^3 + (46056797/1440)*n^2 + (984185/3)*n - 1221248 for n>13

%e Some solutions for 5X5

%e ..1..........1..........1..........0..........0..........0..........1

%e ..0.0........0.0........1.0........0.0........1.1........0.0........0.1

%e ..1.0.0......1.0.0......0.0.0......1.0.1......1.0.0......1.0.0......0.0.0

%e ..0.0.0.1....1.0.0.1....1.0.0.0....0.0.0.1....0.0.0.1....0.0.0.1....0.0.0.1

%e ..1.0.1.0.1..0.0.0.1.1..1.1.0.1.0..1.0.1.0.1..0.0.1.0.1..1.0.1.1.1..1.0.1.1.0

%K nonn

%O 1,5

%A _R. H. Hardin_ Aug 26 2011