A187382 - OEIS

%I #12 Apr 24 2018 08:50:51

%S 0,0,0,404,2140,6380,13220,22996,35366,50330,67888,88040,110786,

%T 136126,164060,194588,227710,263426,301736,342640,386138,432230,

%U 480916,532196,586070,642538,701600,763256,827506,894350,963788,1035820,1110446

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

%H R. H. Hardin, <a href="/A187382/b187382.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 1297*n^2 - 9679*n + 17420 for n>6.

%F Conjectures from _Colin Barker_, Apr 24 2018: (Start)

%F G.f.: 2*x^4*(202 + 464*x + 586*x^2 + 48*x^3 + 168*x^4 - 171*x^5) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.

%F (End)

%e Some solutions for 4 X 4:

%e ..4..2..0..0....0..0..3..0....0..0..0..5....0..4..2..0....0..0..8..0

%e ..5..3..1..0....0..2..4..0....0..2..4..6....7..5..3..1....0..0..5..7

%e ..6..8..0..0....1..0..5..7....0..3..1..7....8..6..0..0....2..4..6..0

%e ..7..0..0..0....0..0..6..8....0..0..0..8....0..0..0..0....3..1..0..0

%Y Row 8 of A187377.

%K nonn

%O 1,4

%A _R. H. Hardin_, Mar 09 2011