A187192 Number of 5-turn rook's tours on an n X n board summed over all starting positions.

0, 0, 720, 9792, 58800, 231840, 705600, 1800960, 4046112, 8251200, 15594480, 27720000, 46846800, 75889632, 118591200, 179665920, 264955200, 381594240, 538190352

Offset

1,3

Links

Table of n, a(n) for n=1..19.

Formula

Empirical: a(n) = 16*n^6 - 98*n^5 + 228*n^4 - 238*n^3 + 92*n^2.

Empirical G.f.: 48*x^3*(15+99*x+112*x^2+14*x^3)/(1-x)^7. [Colin Barker, Jan 22 2012]

Example

Some solutions for 3X3
..0..5..1....0..0..4....0..1..5....1..0..2....1..0..0....4..0..5....2..3..1
..0..0..2....2..0..3....0..3..4....0..5..0....2..0..5....3..0..0....0..0..0
..0..4..3....1..0..5....0..2..0....0..4..3....3..0..4....2..1..0....5..4..0

Crossrefs

Row 5 of A187189.

Sequence in context: A119540 A052784 A052786 * A052792 A052790 A052521

Adjacent sequences: A187189 A187190 A187191 * A187193 A187194 A187195

Keyword

nonn,more

Author

R. H. Hardin, Mar 06 2011

Status

approved