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A187382
Number of 8-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.
1
0, 0, 0, 404, 2140, 6380, 13220, 22996, 35366, 50330, 67888, 88040, 110786, 136126, 164060, 194588, 227710, 263426, 301736, 342640, 386138, 432230, 480916, 532196, 586070, 642538, 701600, 763256, 827506, 894350, 963788, 1035820, 1110446
OFFSET
1,4
LINKS
FORMULA
Empirical: a(n) = 1297*n^2 - 9679*n + 17420 for n>6.
Conjectures from Colin Barker, Apr 24 2018: (Start)
G.f.: 2*x^4*(202 + 464*x + 586*x^2 + 48*x^3 + 168*x^4 - 171*x^5) / (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:
..4..2..0..0....0..0..3..0....0..0..0..5....0..4..2..0....0..0..8..0
..5..3..1..0....0..2..4..0....0..2..4..6....7..5..3..1....0..0..5..7
..6..8..0..0....1..0..5..7....0..3..1..7....8..6..0..0....2..4..6..0
..7..0..0..0....0..0..6..8....0..0..0..8....0..0..0..0....3..1..0..0
CROSSREFS
Row 8 of A187377.
Sequence in context: A185637 A234675 A135791 * A306308 A185638 A332140
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 09 2011
STATUS
approved