A194489 - OEIS

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

%S 0,0,0,13,387,3727,23496,111433,429343,1407755,4061432,10561723,

%T 25208796,55996244,117021864,232070481,439779278,800893832,1408234986,

%U 2400123737,3978154435,6430366713,10161044648,15728568633,23892962265,35675014169

%N Number of ways to arrange 5 nonattacking knights on the lower triangle of an n X n board

%C Column 5 of A194492

%H R. H. Hardin, <a href="/A194489/b194489.txt">Table of n, a(n) for n = 1..68</a>

%F Empirical: a(n) = (1/3840)*n^10 + (1/768)*n^9 - (17/384)*n^8 + (3/128)*n^7 + (951/256)*n^6 - (68939/3840)*n^5 - (1433/12)*n^4 + (230047/192)*n^3 - (149581/240)*n^2 - (718267/30)*n + 72425 for n>10

%e Some solutions for 4X4

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

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

%e ..1.0.1....1.0.1....1.0.1....1.1.1....1.0.0....0.0.0....0.0.0....0.0.1

%e ..0.1.0.1..0.1.0.0..0.1.0.1..0.1.0.0..0.0.0.1..1.0.1.1..1.1.1.1..0.1.1.1

%K nonn

%O 1,4

%A _R. H. Hardin_ Aug 26 2011