A187508 Number of 3-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions

0, 6, 31, 74, 135, 214, 311, 426, 559, 710, 879, 1066, 1271, 1494, 1735, 1994, 2271, 2566, 2879, 3210, 3559, 3926, 4311, 4714, 5135, 5574, 6031, 6506, 6999, 7510, 8039, 8586, 9151, 9734, 10335, 10954, 11591, 12246, 12919, 13610, 14319, 15046, 15791

Offset

1,2

Comments

Row 3 of A187507

Links

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

Formula

Empirical: a(n) = 9*n^2 - 20*n + 10 for n>1.

Empirical G.f.: x^2*(6+13*x-x^2)/(1-x)^3. [Colin Barker, Jan 22 2012]

Example

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

Crossrefs

Sequence in context: A025524 A042841 A215730 * A087725 A273790 A096959

Adjacent sequences: A187505 A187506 A187507 * A187509 A187510 A187511

Keyword

nonn

Author

R. H. Hardin Mar 10 2011

Status

approved