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

1,3

Comments

Row 6 of A187507.

Links

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

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)

Example

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

Crossrefs

Cf. A187507.

Sequence in context: A135181 A220159 A202958 * A185243 A014136 A245435

Adjacent sequences: A187508 A187509 A187510 * A187512 A187513 A187514

Keyword

nonn

Author

R. H. Hardin, Mar 10 2011

Status

approved