A187512 Number of 7-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

0, 0, 20, 330, 1224, 2726, 4807, 7458, 10679, 14470, 18831, 23762, 29263, 35334, 41975, 49186, 56967, 65318, 74239, 83730, 93791, 104422, 115623, 127394, 139735, 152646, 166127, 180178, 194799, 209990, 225751, 242082, 258983, 276454, 294495

Offset: 1

Author

R. H. Hardin, Mar 10 2011

Keywords

• nonn

Comments

Row 7 of A187507.

Examples

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

Links

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

Crossrefs

Cf. A187507.

Formula

Empirical: a(n) = 285*n^2 - 1624*n + 2210 for n>5.

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

G.f.: x^3*(1 + x)*(20 + 250*x + 44*x^2 - 20*x^3 - 9*x^4) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

(End)