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.

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

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