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

Author

R. H. Hardin, Mar 11 2011

Keywords

• nonn

Comments

Row 5 of A187586.

Examples

			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
		

Links

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

Crossrefs

Cf. A187586.

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]