A187513 Number of 8-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

0, 0, 12, 390, 1910, 4880, 9250, 14969, 22026, 30421, 40154, 51225, 63634, 77381, 92466, 108889, 126650, 145749, 166186, 187961, 211074, 235525, 261314, 288441, 316906, 346709, 377850, 410329, 444146, 479301, 515794, 553625, 592794, 633301

Offset: 1

Author

R. H. Hardin, Mar 10 2011

Keywords

• nonn

Comments

Row 8 of A187507.

Examples

			Some solutions for 4X4
..0..7..8..0....0..0..0..0....0..0..0..0....1..0..0..0....5..0..0..0
..4..5..6..0....3..4..5..6....5..0..0..0....2..6..7..8....6..4..2..0
..0..3..1..0....0..2..0..7....6..4..2..0....3..4..5..0....7..8..3..1
..0..0..2..0....0..0..1..8....7..8..3..1....0..0..0..0....0..0..0..0
		

Links

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

Formula

Empirical: a(n) = 669*n^2 - 4316*n + 6681 for n>6.

Empirical g.f.: x^3*(12 + 354*x + 776*x^2 + 308*x^3 - 50*x^4 - 51*x^5 - 11*x^6) / (1 - x)^3. - Colin Barker, Nov 27 2017