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A187592 Number of 9-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions. 1
0, 0, 13, 2792, 27252, 103108, 246792, 458018, 732810, 1069534, 1468190, 1928778, 2451298, 3035750, 3682134, 4390450, 5160698, 5992878, 6886990, 7843034, 8861010, 9940918, 11082758, 12286530, 13552234, 14879870, 16269438, 17720938, 19234370 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Row 9 of A187586.

LINKS

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

FORMULA

Empirical: a(n) = 30966*n^2 - 251630*n + 489234 for n>7.

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

G.f.: x^3*(13 + 2753*x + 18915*x^2 + 29715*x^3 + 16432*x^4 - 286*x^5 - 3976*x^6 - 1634*x^7) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>10.

(End)

EXAMPLE

Some solutions for 4 X 4:

..0..0..7..8....3..0..0..9....0..0..8..9....6..8..9..0....0..4..0..0

..5..6..0..9....4..2..8..0....0..1..6..7....7..5..0..0....0..5..3..1

..2..4..0..0....5..7..1..0....0..2..4..5....4..2..0..0....8..6..0..2

..3..1..0..0....6..0..0..0....0..3..0..0....0..3..1..0....9..7..0..0

CROSSREFS

Cf. A187586.

Sequence in context: A283099 A195537 A203692 * A287036 A208315 A296174

Adjacent sequences:  A187589 A187590 A187591 * A187593 A187594 A187595

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 11 2011

STATUS

approved

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Last modified January 27 00:45 EST 2021. Contains 340443 sequences. (Running on oeis4.)