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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 30 05:36 EDT 2021. Contains 346349 sequences. (Running on oeis4.)