A187508 - OEIS

%I #10 Apr 04 2016 16:14:06

%S 0,6,31,74,135,214,311,426,559,710,879,1066,1271,1494,1735,1994,2271,

%T 2566,2879,3210,3559,3926,4311,4714,5135,5574,6031,6506,6999,7510,

%U 8039,8586,9151,9734,10335,10954,11591,12246,12919,13610,14319,15046,15791

%N Number of 3-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions

%C Row 3 of A187507

%H R. H. Hardin, <a href="/A187508/b187508.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 9*n^2 - 20*n + 10 for n>1.

%F Empirical G.f.: x^2*(6+13*x-x^2)/(1-x)^3. [Colin Barker, Jan 22 2012]

%e Some solutions for 4X4

%e ..0..0..0..0....0..0..0..0....1..0..0..0....0..2..0..0....3..1..0..0

%e ..0..2..3..0....3..0..0..0....2..3..0..0....0..3..1..0....0..2..0..0

%e ..0..0..1..0....0..2..0..0....0..0..0..0....0..0..0..0....0..0..0..0

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Mar 10 2011