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

1,2

Comments

Row 3 of A187850.

Links

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

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)

Example

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

Crossrefs

Cf. A187850.

Sequence in context: A000552 A233876 A171742 * A125436 A096821 A168303

Adjacent sequences: A187848 A187849 A187850 * A187852 A187853 A187854

Keyword

nonn

Author

R. H. Hardin, Mar 14 2011

Status

approved