A187591 Number of 8-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 0, 34, 2309, 15056, 45718, 95776, 164135, 250132, 353767, 475040, 613951, 770500, 944687, 1136512, 1345975, 1573076, 1817815, 2080192, 2360207, 2657860, 2973151, 3306080, 3656647, 4024852, 4410695, 4814176, 5235295, 5674052, 6130447, 6604480

Offset: 1

Author

R. H. Hardin, Mar 11 2011

Keywords

• nonn

Comments

Row 8 of A187586.

Examples

			Some solutions for 4 X 4:
..0..0..6..0....3..1..0..0....0..0..0..0....0..0..6..7....0..0..0..0
..4..5..7..8....4..2..7..8....1..5..6..7....4..5..0..8....1..0..0..6
..0..3..0..0....5..6..0..0....2..3..4..8....2..3..0..0....2..4..5..7
..0..1..2..0....0..0..0..0....0..0..0..0....0..1..0..0....3..0..0..8
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A187586.

Formula

Empirical: a(n) = 8819*n^2 - 63926*n + 111127 for n>6.

Conjectures from Colin Barker, Apr 24 2018: (Start)

G.f.: x^3*(34 + 2207*x + 8231*x^2 + 7443*x^3 + 1481*x^4 - 1095*x^5 - 663*x^6) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.

(End)