A187592 - OEIS

%I #10 Apr 24 2018 14:31:07

%S 0,0,13,2792,27252,103108,246792,458018,732810,1069534,1468190,

%T 1928778,2451298,3035750,3682134,4390450,5160698,5992878,6886990,

%U 7843034,8861010,9940918,11082758,12286530,13552234,14879870,16269438,17720938,19234370

%N Number of 9-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

%C Row 9 of A187586.

%H R. H. Hardin, <a href="/A187592/b187592.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 30966*n^2 - 251630*n + 489234 for n>7.

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

%F G.f.: x^3*(13 + 2753*x + 18915*x^2 + 29715*x^3 + 16432*x^4 - 286*x^5 - 3976*x^6 - 1634*x^7) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.

%F (End)

%e Some solutions for 4 X 4:

%e ..0..0..7..8....3..0..0..9....0..0..8..9....6..8..9..0....0..4..0..0

%e ..5..6..0..9....4..2..8..0....0..1..6..7....7..5..0..0....0..5..3..1

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

%e ..3..1..0..0....6..0..0..0....0..3..0..0....0..3..1..0....9..7..0..0

%Y Cf. A187586.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 11 2011