A187510 Number of 5-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

0, 0, 40, 184, 435, 788, 1243, 1800, 2459, 3220, 4083, 5048, 6115, 7284, 8555, 9928, 11403, 12980, 14659, 16440, 18323, 20308, 22395, 24584, 26875, 29268, 31763, 34360, 37059, 39860, 42763, 45768, 48875, 52084, 55395, 58808, 62323, 65940, 69659, 73480

Offset

1,3

Links

R. H. Hardin, Table of n, a(n) for n = 1..50

Formula

Empirical: a(n) = 51*n^2 - 208*n + 200 for n>3.

Empirical g.f.: x^3*(40+64*x+3*x^2-5*x^3)/(1-x)^3. - Colin Barker, Jan 22 2012

Example

Some solutions for 4X4
..0..0..0..0....0..0..0..0....0..0..0..0....4..0..0..0....0..1..0..0
..0..0..0..0....0..0..0..0....4..5..0..0....5..3..1..0....0..2..0..0
..0..5..3..1....0..0..4..5....2..3..0..0....0..0..2..0....0..3..4..5
..0..0..4..2....0..1..2..3....0..1..0..0....0..0..0..0....0..0..0..0

Crossrefs

Row 5 of A187507.

Sequence in context: A251210 A211497 A251203 * A187379 A077818 A386906

Adjacent sequences: A187507 A187508 A187509 * A187511 A187512 A187513

Keyword

nonn

Author

R. H. Hardin, Mar 10 2011

Status

approved