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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 (list; graph; refs; listen; history; text; internal format)
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: A212023 A056566 A242177 * A160471 A252709 A138590

Adjacent sequences:  A187588 A187589 A187590 * A187592 A187593 A187594

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 11 2011

STATUS

approved

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Last modified June 2 06:13 EDT 2020. Contains 334767 sequences. (Running on oeis4.)