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A188778 Number of 3-turn bishop's tours on an n X n board summed over all starting positions.

%I A188778 #14 Jul 22 2025 11:22:54
%S A188778 0,0,28,152,488,1192,2468,4560,7760,12400,18860,27560,38968,53592,
%T A188778 71988,94752,122528,156000,195900,243000,298120,362120,435908,520432,
%U A188778 616688,725712,848588,986440,1140440,1311800,1501780,1711680,1942848,2196672
%N A188778 Number of 3-turn bishop's tours on an n X n board summed over all starting positions.
%C A188778 Row 3 of A188777
%H A188778 R. H. Hardin, <a href="/A188778/b188778.txt">Table of n, a(n) for n = 1..42</a>
%F A188778 Empirical: a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6)
%F A188778 Contribution from _Vaclav Kotesovec_, Sep 01 2012: (Start)
%F A188778 Empirical: G.f.: 4*x^3*(7 + 10*x + 5*x^2)/((1-x)^5*(1+x))
%F A188778 Empirical: a(n) = 1/4 - 10*n/3 + 23*n^2/3 - 20*n^3/3 + 11*n^4/6 - (-1)^n/4
%F A188778 (End)
%e A188778 Some solutions for 4X4
%e A188778 ..0..0..0..0....0..0..0..1....1..0..0..0....0..0..0..0....0..0..2..0
%e A188778 ..1..0..0..0....0..0..0..0....0..3..0..0....3..0..0..0....0..0..0..3
%e A188778 ..0..3..0..0....0..2..0..0....0..0..0..0....0..1..0..0....1..0..0..0
%e A188778 ..0..0..2..0....0..0..3..0....0..0..0..2....0..0..2..0....0..0..0..0
%K A188778 nonn
%O A188778 1,3
%A A188778 _R. H. Hardin_ Apr 10 2011