A187587 Number of 4-step E, S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 5, 84, 286, 604, 1038, 1588, 2254, 3036, 3934, 4948, 6078, 7324, 8686, 10164, 11758, 13468, 15294, 17236, 19294, 21468, 23758, 26164, 28686, 31324, 34078, 36948, 39934, 43036, 46254, 49588, 53038, 56604, 60286, 64084, 67998, 72028, 76174, 80436, 84814

Offset: 1

Author

R. H. Hardin, Mar 11 2011

Keywords

• nonn
• changed

Examples

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

Links

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

Crossrefs

Row 4 of A187586.

Formula

Empirical: a(n) = 58*n^2 - 204*n + 174 for n>2.

Empirical g.f.: x^2*(5+69*x+49*x^2-7*x^3)/(1-x)^3. - Colin Barker, Jan 22 2012