A187174 Number of 4-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, 8, 48, 176, 384, 664, 1016, 1440, 1936, 2504, 3144, 3856, 4640, 5496, 6424, 7424, 8496, 9640, 10856, 12144, 13504, 14936, 16440, 18016, 19664, 21384, 23176, 25040, 26976, 28984, 31064, 33216, 35440, 37736, 40104, 42544, 45056, 47640, 50296

Offset: 1

Author

R. H. Hardin, Mar 06 2011

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 4 of A187172.

Formula

Empirical: a(n) = 36*n^2 - 260*n + 440 for n>5.

G.f.: 8*x^4*(1 + 3*x + 7*x^2 - x^3 - x^4) / (1 - x)^3 (conjectured). - Colin Barker, Apr 22 2018