A187514 Number of 9-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

0, 0, 6, 450, 2872, 8522, 17564, 29834, 45255, 63814, 85511, 110346, 138319, 169430, 203679, 241066, 281591, 325254, 372055, 421994, 475071, 531286, 590639, 653130, 718759, 787526, 859431, 934474, 1012655, 1093974, 1178431, 1266026, 1356759

Offset: 1

Author

R. H. Hardin, Mar 10 2011

Keywords

• nonn

Comments

Row 9 of A187507.

Examples

			Some solutions for 4 X 4:
..5..6..7..0....5..3..0..0....0..0..0..0....0..0..0..0....1..2..3..0
..3..4..8..9....6..4..2..0....7..8..9..1....3..4..5..6....0..0..4..5
..0..2..0..0....7..8..0..1....0..6..4..2....0..2..9..7....0..0..8..6
..0..0..1..0....0..9..0..0....0..0..5..3....0..0..1..8....0..0..9..7
		

Links

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

Crossrefs

Cf. A187507.

Formula

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

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

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.

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

(End)