A187176 Number of 6-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, 88, 496, 1440, 3064, 5344, 8208, 11640, 15640, 20208, 25344, 31048, 37320, 44160, 51568, 59544, 68088, 77200, 86880, 97128, 107944, 119328, 131280, 143800, 156888, 170544, 184768, 199560, 214920, 230848, 247344, 264408, 282040

Offset

1,6

Comments

Row 6 of A187172.

Links

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

Formula

Empirical: a(n) = 284*n^2 - 3100*n + 7944 for n>9.

G.f.: 8*x^6*(11 + 29*x + 27*x^2 + 18*x^3 - 3*x^4 - 9*x^5 - 2*x^6) / (1 - x)^3 (conjectured). - Colin Barker, Apr 22 2018

Example

Some solutions for 6 X 6:
..0..0..0..5..0..0....0..0..0..0..0..0....0..0..4..0..0..0....0..0..0..6..0..0
..0..6..0..0..0..0....0..0..0..0..6..0....3..0..0..0..0..0....0..1..0..0..0..0
..0..0..0..0..4..0....0..0..5..0..0..0....0..0..0..5..0..0....0..0..0..0..5..0
..0..0..1..0..0..0....4..0..0..0..0..1....0..2..0..0..0..0....0..0..2..0..0..0
..0..0..0..0..0..3....0..0..0..2..0..0....0..0..0..0..6..0....0..0..0..0..0..4
..0..0..0..2..0..0....0..3..0..0..0..0....0..0..1..0..0..0....0..0..0..3..0..0

Crossrefs

Cf. A187172.

Sequence in context: A234770 A052049 A046378 * A236009 A236003 A183839

Adjacent sequences: A187173 A187174 A187175 * A187177 A187178 A187179

Keyword

nonn

Author

R. H. Hardin, Mar 06 2011

Status

approved