A187190 Number of 3-turn rook's tours on an n X n board summed over all starting positions

0, 8, 108, 480, 1400, 3240, 6468, 11648, 19440, 30600, 45980, 66528, 93288, 127400, 170100, 222720, 286688, 363528, 454860, 562400, 687960, 833448, 1000868, 1192320, 1410000, 1656200, 1933308, 2243808, 2590280, 2975400

Offset

1,2

Links

Table of n, a(n) for n=1..30.

Formula

Empirical: a(n) = 4*n^4 - 10*n^3 + 6*n^2.

Empirical G.f.: 4*x^2*(2+17*x+5*x^2)/(1-x)^5. - Colin Barker, Jan 22 2012

Example

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

Crossrefs

Row 3 of A187189.

Sequence in context: A105261 A187288 A275134 * A099762 A246498 A119936

Adjacent sequences: A187187 A187188 A187189 * A187191 A187192 A187193

Keyword

nonn

Author

R. H. Hardin, Mar 06 2011

Status

approved