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A187511 Number of 6-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

%I A187511 #11 Apr 24 2018 09:20:12
%S A187511 0,0,36,272,772,1525,2524,3769,5260,6997,8980,11209,13684,16405,19372,
%T A187511 22585,26044,29749,33700,37897,42340,47029,51964,57145,62572,68245,
%U A187511 74164,80329,86740,93397,100300,107449,114844,122485,130372,138505,146884
%N A187511 Number of 6-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.
%C A187511 Row 6 of A187507.
%H A187511 R. H. Hardin, <a href="/A187511/b187511.txt">Table of n, a(n) for n = 1..50</a>
%F A187511 Empirical: a(n) = 123*n^2 - 600*n + 697 for n>4.
%F A187511 Conjectures from _Colin Barker_, Apr 24 2018: (Start)
%F A187511 G.f.: x^3*(36 + 164*x + 64*x^2 - 11*x^3 - 7*x^4) / (1 - x)^3.
%F A187511 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.
%F A187511 (End)
%e A187511 Some solutions for 4 X 4:
%e A187511 ..0..0..0..0....1..2..0..0....0..0..2..0....0..0..6..0....0..0..6..0
%e A187511 ..5..3..0..0....0..3..0..0....0..0..3..1....0..0..4..5....0..0..4..5
%e A187511 ..6..4..2..0....6..4..0..0....0..0..4..5....0..0..2..3....0..1..2..3
%e A187511 ..0..0..0..1....0..5..0..0....0..0..0..6....0..0..0..1....0..0..0..0
%Y A187511 Cf. A187507.
%K A187511 nonn
%O A187511 1,3
%A A187511 _R. H. Hardin_, Mar 10 2011