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%I #12 Apr 26 2018 08:38:59
%S 0,24,304,1056,2312,4048,6264,8960,12136,15792,19928,24544,29640,
%T 35216,41272,47808,54824,62320,70296,78752,87688,97104,107000,117376,
%U 128232,139568,151384,163680,176456,189712,203448,217664,232360,247536,263192
%N Number of 3-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.
%C Row 3 of A187850.
%H R. H. Hardin, <a href="/A187851/b187851.txt">Table of n, a(n) for n = 1..50</a>
%F Empirical: a(n) = 240*n^2 - 904*n + 832 for n>3.
%F Conjectures from _Colin Barker_, Apr 26 2018: (Start)
%F G.f.: 8*x^2*(3 + 29*x + 27*x^2 + 4*x^3 - 3*x^4) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
%F (End)
%e Some solutions for 4 X 4:
%e ..0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
%e ..0..2..0..0....0..0..2..0....3..0..0..0....0..0..0..0....0..0..0..1
%e ..0..0..0..0....0..3..1..0....0..2..0..0....0..0..2..0....0..2..3..0
%e ..3..0..0..0....0..0..0..0....0..1..0..0....3..1..0..0....0..0..0..0
%Y Cf. A187850.
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 14 2011
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