A187195 Number of 8-turn rook's tours on an n X n board summed over all starting positions.

0, 0, 2664, 551232, 12319200, 118332000, 709921800, 3141298944, 11217854592, 34149988800, 91867386600, 223898241600

Offset

1,3

Links

Table of n, a(n) for n=1..12.

Formula

Empirical: a(n) = 128*n^9 - 1538*n^8 + 7956*n^7 - 23556*n^6 + 44586*n^5 - 55218*n^4 + 40894*n^3 - 13252*n^2.

Empirical G.f.: 72*x^3 * (2599*x^6 +52838*x^5 +213575*x^4 +272580*x^3 +96205*x^2 +7286*x +37) / (x-1)^10. [Colin Barker, Jul 01 2012]

Example

Some solutions for 4X4
..4..2..3..0....0..6..7..5....0..5..0..6....0..2..3..0....2..8..3..0
..5..0..0..8....0..0..0..0....8..0..0..7....7..1..6..8....1..6..5..0
..0..1..0..0....0..1..2..3....0..0..1..0....0..0..5..0....0..7..0..0
..6..0..0..7....0..0..8..4....0..4..2..3....0..0..4..0....0..0..4..0

Crossrefs

Row 8 of A187189.

Sequence in context: A167191 A002482 A187293 * A107532 A110838 A019424

Adjacent sequences: A187192 A187193 A187194 * A187196 A187197 A187198

Keyword

nonn,more

Author

R. H. Hardin, Mar 06 2011

Status

approved