A187288 Number of 3-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

0, 8, 108, 328, 672, 1128, 1696, 2376, 3168, 4072, 5088, 6216, 7456, 8808, 10272, 11848, 13536, 15336, 17248, 19272, 21408, 23656, 26016, 28488, 31072, 33768, 36576, 39496, 42528, 45672, 48928, 52296, 55776, 59368, 63072, 66888, 70816, 74856, 79008

Offset

1,2

Comments

Row 3 of A187286.

Links

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

Formula

Empirical: a(n) = 56*n^2 - 160*n + 72 for n>3.

Conjectures from Colin Barker, Apr 22 2018: (Start)

G.f.: 4*x^2*(2 + 21*x + 7*x^2 + 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..0....0..0..0..0....0..0..0..0....3..0..0..0....0..0..3..2
..2..0..0..0....0..0..0..0....0..0..0..0....2..0..1..0....0..0..0..1
..1..0..0..0....0..0..1..0....1..0..0..0....0..0..0..0....0..0..0..0
..3..0..0..0....3..0..2..0....2..0..3..0....0..0..0..0....0..0..0..0

Crossrefs

Cf. A187286.

Sequence in context: A239985 A274892 A105261 * A275134 A187190 A099762

Adjacent sequences: A187285 A187286 A187287 * A187289 A187290 A187291

Keyword

nonn

Author

R. H. Hardin, Mar 08 2011

Status

approved