A187587 - OEIS

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

%S 0,5,84,286,604,1038,1588,2254,3036,3934,4948,6078,7324,8686,10164,

%T 11758,13468,15294,17236,19294,21468,23758,26164,28686,31324,34078,

%U 36948,39934,43036,46254,49588,53038,56604,60286,64084,67998,72028,76174,80436,84814

%N Number of 4-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions

%C Row 4 of A187586

%H R. H. Hardin, <a href="/A187587/b187587.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 58*n^2 - 204*n + 174 for n>2.

%F Empirical G.f.: x^2*(5+69*x+49*x^2-7*x^3)/(1-x)^3. [Colin Barker, Jan 22 2012]

%e Some solutions for 4X4

%e ..0..0..0..0....0..0..0..0....0..2..0..0....0..0..0..0....0..0..2..4

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

%e ..0..0..2..3....0..0..2..3....0..4..0..0....0..0..2..4....0..0..0..0

%e ..0..0..0..4....0..1..0..4....0..0..0..0....0..1..3..0....0..0..0..0

%K nonn

%O 1,2

%A _R. H. Hardin_ Mar 11 2011