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A187590 Number of 7-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

%I A187590 #11 Apr 24 2018 15:42:14
%S A187590 0,0,78,1708,7666,19104,35832,57592,84384,116208,153064,194952,241872,
%T A187590 293824,350808,412824,479872,551952,629064,711208,798384,890592,
%U A187590 987832,1090104,1197408,1309744,1427112,1549512,1676944,1809408,1946904,2089432
%N A187590 Number of 7-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
%C A187590 Row 7 of A187586.
%H A187590 R. H. Hardin, <a href="/A187590/b187590.txt">Table of n, a(n) for n = 1..50</a>
%F A187590 Empirical: a(n) = 2516*n^2 - 15980*n + 24408 for n>5.
%F A187590 Conjectures from _Colin Barker_, Apr 24 2018: (Start)
%F A187590 G.f.: 2*x^3*(39 + 737*x + 1388*x^2 + 576*x^3 - 95*x^4 - 129*x^5) / (1 - x)^3.
%F A187590 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
%F A187590 (End)
%e A187590 Some solutions for 4 X 4:
%e A187590 ..0..0..0..0....0..0..0..5....0..0..3..0....1..0..0..0....0..0..0..0
%e A187590 ..0..0..0..0....0..0..4..6....0..2..4..0....2..3..5..7....0..0..0..0
%e A187590 ..1..3..0..6....2..3..0..7....1..7..5..0....0..4..6..0....1..3..5..0
%e A187590 ..2..4..5..7....0..1..0..0....0..0..6..0....0..0..0..0....2..4..6..7
%Y A187590 Cf. A187586.
%K A187590 nonn
%O A187590 1,3
%A A187590 _R. H. Hardin_, Mar 11 2011