A187588 Number of 5-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 0, 106, 578, 1484, 2794, 4508, 6626, 9148, 12074, 15404, 19138, 23276, 27818, 32764, 38114, 43868, 50026, 56588, 63554, 70924, 78698, 86876, 95458, 104444, 113834, 123628, 133826, 144428, 155434, 166844, 178658, 190876, 203498, 216524

Offset

1,3

Comments

Row 5 of A187586.

Links

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

Formula

Empirical: a(n) = 202*n^2 - 912*n + 994 for n>3.

Empirical G.f.: 2*x^3*(53+130*x+34*x^2-15*x^3)/(1-x)^3. [Colin Barker, Jan 22 2012]

Example

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

Crossrefs

Cf. A187586.

Sequence in context: A234421 A234414 A090037 * A051974 A188837 A184217

Adjacent sequences: A187585 A187586 A187587 * A187589 A187590 A187591

Keyword

nonn

Author

R. H. Hardin, Mar 11 2011

Status

approved