A187378 Number of 4-step S, NW and NE-moving king's tours on an n X n board summed over all starting positions.

0, 4, 40, 132, 278, 478, 732, 1040, 1402, 1818, 2288, 2812, 3390, 4022, 4708, 5448, 6242, 7090, 7992, 8948, 9958, 11022, 12140, 13312, 14538, 15818, 17152, 18540, 19982, 21478, 23028, 24632, 26290, 28002, 29768, 31588, 33462, 35390, 37372, 39408, 41498, 43642

Offset: 1

Author

R. H. Hardin, Mar 09 2011

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Row 4 of A187377.

Formula

Empirical: a(n) = 27*n^2 - 97*n + 88 for n>2.

Empirical g.f.: 2*x^2*(2+14*x+12*x^2-x^3)/(1-x)^3. - Colin Barker, Jan 22 2012