A187382 Number of 8-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 0, 0, 404, 2140, 6380, 13220, 22996, 35366, 50330, 67888, 88040, 110786, 136126, 164060, 194588, 227710, 263426, 301736, 342640, 386138, 432230, 480916, 532196, 586070, 642538, 701600, 763256, 827506, 894350, 963788, 1035820, 1110446

Offset: 1

Author

R. H. Hardin, Mar 09 2011

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 8 of A187377.

Formula

Empirical: a(n) = 1297*n^2 - 9679*n + 17420 for n>6.

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

G.f.: 2*x^4*(202 + 464*x + 586*x^2 + 48*x^3 + 168*x^4 - 171*x^5) / (1 - x)^3.

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

(End)