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

1,3

Comments

Row 9 of A187507.

Links

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

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)

Example

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

Crossrefs

Cf. A187507.

Sequence in context: A001328 A174777 A265168 * A258873 A244195 A338943

Adjacent sequences: A187511 A187512 A187513 * A187515 A187516 A187517

Keyword

nonn

Author

R. H. Hardin, Mar 10 2011

Status

approved