A187851 Number of 3-step king-knight's tours (piece capable of both kinds of moves) on an n X n board summed over all starting positions.

0, 24, 304, 1056, 2312, 4048, 6264, 8960, 12136, 15792, 19928, 24544, 29640, 35216, 41272, 47808, 54824, 62320, 70296, 78752, 87688, 97104, 107000, 117376, 128232, 139568, 151384, 163680, 176456, 189712, 203448, 217664, 232360, 247536, 263192

Offset: 1

Author

R. H. Hardin, Mar 14 2011

Keywords

• nonn

Comments

Row 3 of A187850.

Examples

			Some solutions for 4 X 4:
..0..0..0..1....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..2..0..0....0..0..2..0....3..0..0..0....0..0..0..0....0..0..0..1
..0..0..0..0....0..3..1..0....0..2..0..0....0..0..2..0....0..2..3..0
..3..0..0..0....0..0..0..0....0..1..0..0....3..1..0..0....0..0..0..0
		

Links

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

Crossrefs

Cf. A187850.

Formula

Empirical: a(n) = 240*n^2 - 904*n + 832 for n>3.

Conjectures from Colin Barker, Apr 26 2018: (Start)

G.f.: 8*x^2*(3 + 29*x + 27*x^2 + 4*x^3 - 3*x^4) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.

(End)