cp's OEIS Frontend

A187382 Number of 8-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

%I A187382 #12 Apr 24 2018 08:50:51
%S A187382 0,0,0,404,2140,6380,13220,22996,35366,50330,67888,88040,110786,
%T A187382 136126,164060,194588,227710,263426,301736,342640,386138,432230,
%U A187382 480916,532196,586070,642538,701600,763256,827506,894350,963788,1035820,1110446
%N A187382 Number of 8-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
%H A187382 R. H. Hardin, <a href="/A187382/b187382.txt">Table of n, a(n) for n = 1..50</a>
%F A187382 Empirical: a(n) = 1297*n^2 - 9679*n + 17420 for n>6.
%F A187382 Conjectures from _Colin Barker_, Apr 24 2018: (Start)
%F A187382 G.f.: 2*x^4*(202 + 464*x + 586*x^2 + 48*x^3 + 168*x^4 - 171*x^5) / (1 - x)^3.
%F A187382 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.
%F A187382 (End)
%e A187382 Some solutions for 4 X 4:
%e A187382 ..4..2..0..0....0..0..3..0....0..0..0..5....0..4..2..0....0..0..8..0
%e A187382 ..5..3..1..0....0..2..4..0....0..2..4..6....7..5..3..1....0..0..5..7
%e A187382 ..6..8..0..0....1..0..5..7....0..3..1..7....8..6..0..0....2..4..6..0
%e A187382 ..7..0..0..0....0..0..6..8....0..0..0..8....0..0..0..0....3..1..0..0
%Y A187382 Row 8 of A187377.
%K A187382 nonn
%O A187382 1,4
%A A187382 _R. H. Hardin_, Mar 09 2011