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A187591 Number of 8-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

%I A187591 #11 Apr 24 2018 23:15:31
%S A187591 0,0,34,2309,15056,45718,95776,164135,250132,353767,475040,613951,
%T A187591 770500,944687,1136512,1345975,1573076,1817815,2080192,2360207,
%U A187591 2657860,2973151,3306080,3656647,4024852,4410695,4814176,5235295,5674052,6130447,6604480
%N A187591 Number of 8-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
%C A187591 Row 8 of A187586.
%H A187591 R. H. Hardin, <a href="/A187591/b187591.txt">Table of n, a(n) for n = 1..50</a>
%F A187591 Empirical: a(n) = 8819*n^2 - 63926*n + 111127 for n>6.
%F A187591 Conjectures from _Colin Barker_, Apr 24 2018: (Start)
%F A187591 G.f.: x^3*(34 + 2207*x + 8231*x^2 + 7443*x^3 + 1481*x^4 - 1095*x^5 - 663*x^6) / (1 - x)^3.
%F A187591 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.
%F A187591 (End)
%e A187591 Some solutions for 4 X 4:
%e A187591 ..0..0..6..0....3..1..0..0....0..0..0..0....0..0..6..7....0..0..0..0
%e A187591 ..4..5..7..8....4..2..7..8....1..5..6..7....4..5..0..8....1..0..0..6
%e A187591 ..0..3..0..0....5..6..0..0....2..3..4..8....2..3..0..0....2..4..5..7
%e A187591 ..0..1..2..0....0..0..0..0....0..0..0..0....0..1..0..0....3..0..0..8
%Y A187591 Cf. A187586.
%K A187591 nonn
%O A187591 1,3
%A A187591 _R. H. Hardin_, Mar 11 2011