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

1,2

Comments

Row 4 of A187189

Links

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

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]

Example

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

Crossrefs

Sequence in context: A060355 A060859 A187289 * A054607 A254408 A132592

Adjacent sequences: A187188 A187189 A187190 * A187192 A187193 A187194

Keyword

nonn

Author

R. H. Hardin Mar 06 2011

Status

approved