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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 06 2011
STATUS
approved