A187193 Number of 6-turn rook's tours on an n X n board summed over all starting positions.

0, 0, 1440, 40896, 364800, 1902240, 7197120, 21960960, 57407616, 133531200, 283488480, 559247040, 1038660480

Offset

1,3

Links

Table of n, a(n) for n=1..13.

Formula

Empirical: a(n) = 32*n^7 - 258*n^6 + 846*n^5 - 1426*n^4 + 1234*n^3 - 428*n^2.

Empirical G.f.: 96*x^3*(15+306*x+812*x^2+503*x^3+44*x^4)/(1-x)^8. [Colin Barker, Jan 22 2012]

Example

Some solutions for 3X3
..0..0..1....0..0..6....3..2..1....0..0..1....0..4..5....0..0..3....0..3..2
..3..4..2....0..4..5....0..0..0....4..6..5....1..0..0....0..5..4....6..0..0
..0..5..6....2..3..1....4..5..6....3..0..2....2..3..6....1..6..2....5..4..1

Crossrefs

Row 6 of A187189.

Sequence in context: A061221 A238041 A187291 * A223108 A023102 A289633

Adjacent sequences: A187190 A187191 A187192 * A187194 A187195 A187196

Keyword

nonn,more

Author

R. H. Hardin, Mar 06 2011

Status

approved