A187509 Number of 4-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

0, 2, 36, 115, 236, 399, 604, 851, 1140, 1471, 1844, 2259, 2716, 3215, 3756, 4339, 4964, 5631, 6340, 7091, 7884, 8719, 9596, 10515, 11476, 12479, 13524, 14611, 15740, 16911, 18124, 19379, 20676, 22015, 23396, 24819, 26284, 27791, 29340, 30931, 32564, 34239

Offset: 1

Author

R. H. Hardin, Mar 10 2011

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 4 of A187507.

Formula

Empirical: a(n) = 21*n^2 - 68*n + 51 for n>2.

Empirical g.f.: x^2*(2+30*x+13*x^2-3*x^3)/(1-x)^3. - Colin Barker, Jan 22 2012