A194487 - OEIS

%I #10 May 05 2018 08:07:57

%S 0,1,12,62,253,804,2136,4958,10376,20013,36144,61846,101163,159286,

%T 242748,359634,519806,735143,1019796,1390458,1866649,2471016,3229648,

%U 4172406,5333268,6750689,8467976,10533678,13001991,15933178,19394004

%N Number of ways to arrange 3 nonattacking knights on the lower triangle of an n X n board.

%C Column 3 of A194492.

%H R. H. Hardin, <a href="/A194487/b194487.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = (1/48)*n^6 + (1/16)*n^5 - (17/16)*n^4 + (133/48)*n^3 + (433/24)*n^2 - (743/6)*n + 218 for n>4.

%F Empirical g.f.: x^2*(1 + 5*x - x^2 + 36*x^3 - 50*x^4 + 50*x^5 - 40*x^6 + 22*x^7 - 12*x^8 + 4*x^9) / (1 - x)^7. - _Colin Barker_, May 05 2018

%e Some solutions for 3 X 3:

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

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

%e ..1.0.0..1.0.0..0.0.0..1.0.0..0.1.1..1.0.1..0.0.1..1.1.0..0.1.0..1.1.1..1.0.1

%Y Cf. A194492.

%K nonn

%O 1,3

%A _R. H. Hardin_, Aug 26 2011