A188778 - OEIS

%I #12 Apr 04 2016 16:14:07

%S 0,0,28,152,488,1192,2468,4560,7760,12400,18860,27560,38968,53592,

%T 71988,94752,122528,156000,195900,243000,298120,362120,435908,520432,

%U 616688,725712,848588,986440,1140440,1311800,1501780,1711680,1942848,2196672

%N Number of 3-turn bishop's tours on an n X n board summed over all starting positions

%C Row 3 of A188777

%H R. H. Hardin, <a href="/A188778/b188778.txt">Table of n, a(n) for n = 1..42</a>

%F Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6)

%F Contribution from _Vaclav Kotesovec_, Sep 01 2012: (Start)

%F Empirical: G.f.: 4*x^3*(7 + 10*x + 5*x^2)/((1-x)^5*(1+x))

%F Empirical: a(n) = 1/4 - 10*n/3 + 23*n^2/3 - 20*n^3/3 + 11*n^4/6 - (-1)^n/4

%F (End)

%e Some solutions for 4X4

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

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

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

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

%K nonn

%O 1,3

%A _R. H. Hardin_ Apr 10 2011