A187191 Number of 4-turn rook's tours on an n X n board summed over all starting positions.

0, 8, 288, 2208, 9200, 27720, 68208, 146048, 282528, 505800, 851840, 1365408, 2101008, 3123848, 4510800, 6351360, 8748608, 11820168, 15699168, 20535200, 26495280, 33764808, 42548528, 53071488, 65580000, 80342600, 97651008

Offset: 1

Author

R. H. Hardin, Mar 06 2011

Keywords

• nonn

Examples

			Some solutions for 3X3
..0..4..0....2..1..0....0..1..2....1..0..0....0..0..4....4..2..3....3..2..0
..2..3..1....3..0..0....4..0..3....2..3..4....0..1..2....0..0..0....0..0..0
..0..0..0....4..0..0....0..0..0....0..0..0....0..0..3....0..1..0....4..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..28

Crossrefs

Row 4 of A187189.

Formula

Empirical: a(n) = 8*n^5 - 34*n^4 + 48*n^3 - 22*n^2.

Empirical g.f.: 8*x^2*(1+30*x+75*x^2+14*x^3)/(1-x)^6. - Colin Barker, Jan 22 2012