A187379 Number of 5-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 0, 40, 188, 487, 924, 1499, 2212, 3063, 4052, 5179, 6444, 7847, 9388, 11067, 12884, 14839, 16932, 19163, 21532, 24039, 26684, 29467, 32388, 35447, 38644, 41979, 45452, 49063, 52812, 56699, 60724, 64887, 69188, 73627, 78204, 82919, 87772, 92763, 97892

Offset

1,3

Links

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

Formula

Empirical: a(n) = 69*n^2 - 322*n + 372 for n>3.

Empirical g.f.: x^3*(40+68*x+43*x^2-13*x^3)/(1-x)^3. - Colin Barker, Jan 22 2012

Example

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

Crossrefs

Row 5 of A187377.

Sequence in context: A211497 A251203 A187510 * A077818 A386906 A387645

Adjacent sequences: A187376 A187377 A187378 * A187380 A187381 A187382

Keyword

nonn

Author

R. H. Hardin, Mar 09 2011

Status

approved