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Number of 4-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions
1

%I #10 Apr 04 2016 16:14:05

%S 0,4,40,132,278,478,732,1040,1402,1818,2288,2812,3390,4022,4708,5448,

%T 6242,7090,7992,8948,9958,11022,12140,13312,14538,15818,17152,18540,

%U 19982,21478,23028,24632,26290,28002,29768,31588,33462,35390,37372,39408

%N Number of 4-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions

%C Row 4 of A187377

%H R. H. Hardin, <a href="/A187378/b187378.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 27*n^2 - 97*n + 88 for n>2.

%F Empirical G.f.: 2*x^2*(2+14*x+12*x^2-x^3)/(1-x)^3. [Colin Barker, Jan 22 2012]

%e Some solutions for 4X4

%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..2....4..0..0..0

%e ..3..0..0..0....0..0..2..0....0..0..0..0....0..0..1..3....0..3..0..0

%e ..4..2..0..0....0..0..3..1....3..1..0..0....0..0..0..4....0..0..2..0

%e ..0..0..1..0....0..0..4..0....4..2..0..0....0..0..0..0....0..0..0..1

%K nonn

%O 1,2

%A _R. H. Hardin_ Mar 09 2011