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A187380 Number of 6-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

%I A187380 #12 Apr 24 2018 06:43:40
%S A187380 0,0,24,264,832,1810,3154,4864,6940,9382,12190,15364,18904,22810,
%T A187380 27082,31720,36724,42094,47830,53932,60400,67234,74434,82000,89932,
%U A187380 98230,106894,115924,125320,135082,145210,155704,166564,177790,189382,201340
%N A187380 Number of 6-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
%H A187380 R. H. Hardin, <a href="/A187380/b187380.txt">Table of n, a(n) for n = 1..50</a>
%F A187380 Empirical: a(n) = 183*n^2 - 1035*n + 1432 for n>4.
%F A187380 Conjectures from _Colin Barker_, Apr 24 2018: (Start)
%F A187380 G.f.: 2*x^3*(12 + 96*x + 56*x^2 + 41*x^3 - 22*x^4) / (1 - x)^3.
%F A187380 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
%F A187380 (End)
%e A187380 Some solutions for 4 X 4:
%e A187380 ..0..6..4..0....4..0..0..0....0..1..0..0....0..5..0..0....0..1..0..0
%e A187380 ..1..3..5..0....5..3..0..0....0..2..0..0....4..6..0..0....0..2..0..6
%e A187380 ..2..0..0..0....6..0..2..0....0..3..5..0....1..3..0..0....0..3..5..0
%e A187380 ..0..0..0..0....0..0..0..1....0..4..6..0....2..0..0..0....0..4..0..0
%Y A187380 Row 6 of A187377.
%K A187380 nonn
%O A187380 1,3
%A A187380 _R. H. Hardin_, Mar 09 2011