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A187178 Number of 8-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions. 1
0, 0, 0, 0, 0, 0, 280, 1784, 5944, 14072, 27104, 45288, 68400, 96048, 128064, 164424, 205128, 250176, 299568, 353304, 411384, 473808, 540576, 611688, 687144, 766944, 851088, 939576, 1032408, 1129584, 1231104, 1336968, 1447176, 1561728, 1680624 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Row 8 of A187172.

LINKS

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

FORMULA

Empirical: a(n) = 2172*n^2 - 30972*n + 103944 for n>13.

Empirical g.f.: 8*x^7*(35 + 118*x + 179*x^2 + 164*x^3 + 117*x^4 + 31*x^5 - 28*x^6 - 49*x^7 - 21*x^8 - 3*x^9) / (1 - x)^3. - Colin Barker, Apr 22 2018

EXAMPLE

Some solutions for 7 X 7:

..0..0..0..4..0..0..0....0..0..0..0..4..0..0....0..0..0..0..0..0..0

..0..5..0..0..0..0..0....0..0..3..0..0..0..0....0..0..0..0..8..0..0

..0..0..0..0..3..0..0....2..0..0..0..0..5..0....0..0..7..0..0..0..0

..0..0..6..0..0..0..0....0..0..0..8..0..0..0....6..0..0..0..0..1..0

..7..0..0..0..0..2..0....0..1..0..0..0..0..6....0..0..0..4..0..0..0

..0..0..0..1..0..0..0....0..0..0..0..7..0..0....0..5..0..0..0..0..2

..0..8..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..0..3..0..0

CROSSREFS

Cf. A187172.

Sequence in context: A242039 A234911 A234905 * A233724 A233718 A272982

Adjacent sequences:  A187175 A187176 A187177 * A187179 A187180 A187181

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 06 2011

STATUS

approved

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Last modified May 16 14:38 EDT 2022. Contains 353704 sequences. (Running on oeis4.)