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%I #10 Apr 26 2018 08:38:44
%S 0,24,1400,7620,20952,41652,69456,104268,146088,194916,250752,313596,
%T 383448,460308,544176,635052,732936,837828,949728,1068636,1194552,
%U 1327476,1467408,1614348,1768296,1929252,2097216,2272188,2454168,2643156
%N Number of 4-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 4 of A187850.
%H R. H. Hardin, <a href="/A187852/b187852.txt">Table of n, a(n) for n = 1..50</a>
%F Empirical: a(n) = 3504*n^2 - 17748*n + 21996 for n>5.
%F Conjectures from _Colin Barker_, Apr 26 2018: (Start)
%F G.f.: 4*x^2*(6 + 332*x + 873*x^2 + 567*x^3 + 64*x^4 - 66*x^5 - 24*x^6) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.
%F (End)
%e Some solutions for 4 X 4:
%e ..0..0..0..0....0..0..2..0....0..0..0..0....0..2..3..0....0..4..0..0
%e ..0..0..0..1....0..0..1..0....0..0..2..0....0..0..4..0....1..0..0..0
%e ..0..3..2..0....0..0..0..3....3..0..0..1....1..0..0..0....0..0..3..0
%e ..0..0..0..4....0..4..0..0....4..0..0..0....0..0..0..0....0..2..0..0
%Y Cf. A187850.
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 14 2011
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