A187591 Number of 8-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 0, 34, 2309, 15056, 45718, 95776, 164135, 250132, 353767, 475040, 613951, 770500, 944687, 1136512, 1345975, 1573076, 1817815, 2080192, 2360207, 2657860, 2973151, 3306080, 3656647, 4024852, 4410695, 4814176, 5235295, 5674052, 6130447, 6604480

Offset

1,3

Comments

Row 8 of A187586.

Links

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

Formula

Empirical: a(n) = 8819*n^2 - 63926*n + 111127 for n>6.

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

G.f.: x^3*(34 + 2207*x + 8231*x^2 + 7443*x^3 + 1481*x^4 - 1095*x^5 - 663*x^6) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>9.

(End)

Example

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

Crossrefs

Cf. A187586.

Sequence in context: A056566 A335090 A242177 * A160471 A252709 A138590

Adjacent sequences: A187588 A187589 A187590 * A187592 A187593 A187594

Keyword

nonn

Author

R. H. Hardin, Mar 11 2011

Status

approved