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A187589 Number of 6-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

%I A187589 #10 Apr 24 2018 15:28:33
%S A187589 0,0,104,1069,3514,7480,12874,19696,27946,37624,48730,61264,75226,
%T A187589 90616,107434,125680,145354,166456,188986,212944,238330,265144,293386,
%U A187589 323056,354154,386680,420634,456016,492826,531064,570730,611824,654346,698296
%N A187589 Number of 6-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
%C A187589 Row 6 of A187586.
%H A187589 R. H. Hardin, <a href="/A187589/b187589.txt">Table of n, a(n) for n = 1..50</a>
%F A187589 Empirical: a(n) = 714*n^2 - 3888*n + 5104 for n>4.
%F A187589 Conjectures from _Colin Barker_, Apr 24 2018: (Start)
%F A187589 G.f.: x^3*(104 + 757*x + 619*x^2 + 41*x^3 - 93*x^4) / (1 - x)^3.
%F A187589 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
%F A187589 (End)
%e A187589 Some solutions for 4 X 4:
%e A187589 ..0..0..0..0....0..0..0..6....0..0..0..4....0..1..2..0....0..0..6..0
%e A187589 ..0..0..6..0....0..4..5..0....0..2..3..5....0..0..3..0....1..3..4..5
%e A187589 ..1..3..4..5....0..1..3..0....0..0..1..6....0..0..4..5....2..0..0..0
%e A187589 ..2..0..0..0....0..2..0..0....0..0..0..0....0..0..0..6....0..0..0..0
%Y A187589 Cf. A187586.
%K A187589 nonn
%O A187589 1,3
%A A187589 _R. H. Hardin_, Mar 11 2011