login
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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 11 2011
STATUS
approved