A187173 Number of 3-step left-handed knight's tours (moves only out two, left one) on an n X n board summed over all starting positions.

0, 0, 0, 16, 60, 128, 220, 336, 476, 640, 828, 1040, 1276, 1536, 1820, 2128, 2460, 2816, 3196, 3600, 4028, 4480, 4956, 5456, 5980, 6528, 7100, 7696, 8316, 8960, 9628, 10320, 11036, 11776, 12540, 13328, 14140, 14976, 15836, 16720, 17628, 18560, 19516, 20496

Offset

1,4

Comments

Row 3 of A187172.

Links

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

Formula

Empirical: a(n) = 12*n^2 - 64*n + 80 for n>3.

G.f.: 4*x^4*(4 - x)*(1 + x) / (1 - x)^3 (conjectured). - Colin Barker, Apr 22 2018

Example

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

Crossrefs

Cf. A187172.

Sequence in context: A027117 A292537 A258730 * A296958 A258731 A316125

Adjacent sequences: A187170 A187171 A187172 * A187174 A187175 A187176

Keyword

nonn

Author

R. H. Hardin, Mar 06 2011

Status

approved