A187590 Number of 7-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 0, 78, 1708, 7666, 19104, 35832, 57592, 84384, 116208, 153064, 194952, 241872, 293824, 350808, 412824, 479872, 551952, 629064, 711208, 798384, 890592, 987832, 1090104, 1197408, 1309744, 1427112, 1549512, 1676944, 1809408, 1946904, 2089432

Offset

1,3

Comments

Row 7 of A187586.

Links

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

Formula

Empirical: a(n) = 2516*n^2 - 15980*n + 24408 for n>5.

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

G.f.: 2*x^3*(39 + 737*x + 1388*x^2 + 576*x^3 - 95*x^4 - 129*x^5) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

(End)

Example

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

Crossrefs

Cf. A187586.

Sequence in context: A230521 A264362 A160839 * A172217 A036524 A262063

Adjacent sequences: A187587 A187588 A187589 * A187591 A187592 A187593

Keyword

nonn

Author

R. H. Hardin, Mar 11 2011

Status

approved