A187175 Number of 5-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, 16, 136, 456, 1024, 1804, 2784, 3964, 5344, 6924, 8704, 10684, 12864, 15244, 17824, 20604, 23584, 26764, 30144, 33724, 37504, 41484, 45664, 50044, 54624, 59404, 64384, 69564, 74944, 80524, 86304, 92284, 98464, 104844, 111424, 118204, 125184

Offset: 1

Author

R. H. Hardin, Mar 06 2011

Keywords

• nonn

Comments

Row 5 of A187172.

Examples

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

Links

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

Crossrefs

Cf. A187172.

Formula

Empirical: a(n) = 100*n^2 - 920*n + 1984 for n>7.

G.f.: 4*x^5*(2 - x)*(2 + 12*x + 18*x^2 + 15*x^3 + 3*x^4) / (1 - x)^3 (conjectured). - Colin Barker, Apr 22 2018