A187589 Number of 6-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 0, 104, 1069, 3514, 7480, 12874, 19696, 27946, 37624, 48730, 61264, 75226, 90616, 107434, 125680, 145354, 166456, 188986, 212944, 238330, 265144, 293386, 323056, 354154, 386680, 420634, 456016, 492826, 531064, 570730, 611824, 654346, 698296

Offset

1,3

Comments

Row 6 of A187586.

Links

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

Formula

Empirical: a(n) = 714*n^2 - 3888*n + 5104 for n>4.

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

G.f.: x^3*(104 + 757*x + 619*x^2 + 41*x^3 - 93*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....0..0..0..6....0..0..0..4....0..1..2..0....0..0..6..0
..0..0..6..0....0..4..5..0....0..2..3..5....0..0..3..0....1..3..4..5
..1..3..4..5....0..1..3..0....0..0..1..6....0..0..4..5....2..0..0..0
..2..0..0..0....0..2..0..0....0..0..0..0....0..0..0..6....0..0..0..0

Crossrefs

Cf. A187586.

Sequence in context: A230028 A340898 A132434 * A200196 A234219 A223420

Adjacent sequences: A187586 A187587 A187588 * A187590 A187591 A187592

Keyword

nonn

Author

R. H. Hardin, Mar 11 2011

Status

approved