A194488 - OEIS

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

%S 0,0,4,46,407,2168,8685,28376,79611,198334,449336,942072,1852096,

%T 3449261,6133944,10482661,17304542,27710241,43194961,65737379,

%U 97916361,143047462,205341311,290086086,403856389,554750936,752661582,1009576306,1339918886

%N Number of ways to arrange 4 nonattacking knights on the lower triangle of an n X n board

%C Column 4 of A194492

%H R. H. Hardin, <a href="/A194488/b194488.txt">Table of n, a(n) for n = 1..117</a>

%F Empirical: a(n) = (1/384)*n^8 + (1/96)*n^7 - (17/64)*n^6 + (5/12)*n^5 + (1571/128)*n^4 - (6653/96)*n^3 - (8641/96)*n^2 + (13951/8)*n - 4161 for n>7

%e Some solutions for 4X4

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

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

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

%e ..0.1.0.1..0.0.0.0..0.0.1.1..0.0.0.1..1.1.0.1..1.0.1.1..0.1.1.1..1.0.1.1

%K nonn

%O 1,3

%A _R. H. Hardin_ Aug 26 2011