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A187515 Number of 10-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

%I A187515 #10 Apr 24 2018 11:08:39
%S A187515 0,0,0,398,3868,13796,31548,56952,89684,129637,176796,231161,292732,
%T A187515 361509,437492,520681,611076,708677,813484,925497,1044716,1171141,
%U A187515 1304772,1445609,1593652,1748901,1911356,2081017,2257884,2441957,2633236
%N A187515 Number of 10-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.
%C A187515 Row 10 of A187507.
%H A187515 R. H. Hardin, <a href="/A187515/b187515.txt">Table of n, a(n) for n = 1..50</a>
%F A187515 Empirical: a(n) = 3603*n^2 - 28504*n + 54377 for n>8.
%F A187515 Conjectures from _Colin Barker_, Apr 24 2018: (Start)
%F A187515 G.f.: x^4*(398 + 2674*x + 3386*x^2 + 1366*x^3 - 172*x^4 - 324*x^5 - 107*x^6 - 15*x^7) / (1 - x)^3.
%F A187515 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.
%F A187515 (End)
%e A187515 Some solutions for 4 X 4:
%e A187515 ..1..0..0..0....7..8..9.10....0..7..8..9....0..5..0..1....0..0..0..1
%e A187515 ..2..3..4..5....0..6..0..0....4..5..6.10....8..6..4..2....0..0..0..2
%e A187515 ..0.10..8..6....0..4..5..0....0..3..1..0....9..7..0..3....9..7..5..3
%e A187515 ..0..0..9..7....1..2..3..0....0..0..2..0...10..0..0..0...10..8..6..4
%Y A187515 Cf. A187507.
%K A187515 nonn
%O A187515 1,4
%A A187515 _R. H. Hardin_, Mar 10 2011