A187511 Number of 6-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

0, 0, 36, 272, 772, 1525, 2524, 3769, 5260, 6997, 8980, 11209, 13684, 16405, 19372, 22585, 26044, 29749, 33700, 37897, 42340, 47029, 51964, 57145, 62572, 68245, 74164, 80329, 86740, 93397, 100300, 107449, 114844, 122485, 130372, 138505, 146884

Offset: 1

Author

R. H. Hardin, Mar 10 2011

Keywords

• nonn

Comments

Row 6 of A187507.

Examples

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

Links

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

Crossrefs

Cf. A187507.

Formula

Empirical: a(n) = 123*n^2 - 600*n + 697 for n>4.

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

G.f.: x^3*(36 + 164*x + 64*x^2 - 11*x^3 - 7*x^4) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>7.

(End)