A187515 Number of 10-step S, E, and NW-moving king's tours on an n X n board summed over all starting positions.

0, 0, 0, 398, 3868, 13796, 31548, 56952, 89684, 129637, 176796, 231161, 292732, 361509, 437492, 520681, 611076, 708677, 813484, 925497, 1044716, 1171141, 1304772, 1445609, 1593652, 1748901, 1911356, 2081017, 2257884, 2441957, 2633236

Offset: 1

Author

R. H. Hardin, Mar 10 2011

Keywords

• nonn

Comments

Row 10 of A187507.

Examples

			Some solutions for 4 X 4:
..1..0..0..0....7..8..9.10....0..7..8..9....0..5..0..1....0..0..0..1
..2..3..4..5....0..6..0..0....4..5..6.10....8..6..4..2....0..0..0..2
..0.10..8..6....0..4..5..0....0..3..1..0....9..7..0..3....9..7..5..3
..0..0..9..7....1..2..3..0....0..0..2..0...10..0..0..0...10..8..6..4
		

Links

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

Crossrefs

Cf. A187507.

Formula

Empirical: a(n) = 3603*n^2 - 28504*n + 54377 for n>8.

Conjectures from Colin Barker, Apr 24 2018: (Start)

G.f.: x^4*(398 + 2674*x + 3386*x^2 + 1366*x^3 - 172*x^4 - 324*x^5 - 107*x^6 - 15*x^7) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>11.

(End)