A187514 - OEIS

%I #10 Apr 24 2018 11:08:46

%S 0,0,6,450,2872,8522,17564,29834,45255,63814,85511,110346,138319,

%T 169430,203679,241066,281591,325254,372055,421994,475071,531286,

%U 590639,653130,718759,787526,859431,934474,1012655,1093974,1178431,1266026,1356759

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

%C Row 9 of A187507.

%H R. H. Hardin, <a href="/A187514/b187514.txt">Table of n, a(n) for n = 1..50</a>

%F Empirical: a(n) = 1569*n^2 - 11252*n + 19434 for n>7.

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

%F G.f.: x^3*(6 + 432*x + 1540*x^2 + 1250*x^3 + 164*x^4 - 164*x^5 - 77*x^6 - 13*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 ..5..6..7..0....5..3..0..0....0..0..0..0....0..0..0..0....1..2..3..0

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

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

%e ..0..0..1..0....0..9..0..0....0..0..5..3....0..0..1..8....0..0..9..7

%Y Cf. A187507.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 10 2011