A187289 Number of 4-step one or two space at a time rook's tours on an n X n board summed over all starting positions.

0, 8, 288, 1256, 3084, 5712, 9120, 13288, 18216, 23904, 30352, 37560, 45528, 54256, 63744, 73992, 85000, 96768, 109296, 122584, 136632, 151440, 167008, 183336, 200424, 218272, 236880, 256248, 276376, 297264, 318912, 341320, 364488, 388416

Offset

1,2

Comments

Row 4 of A187286.

Links

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

Formula

Empirical: a(n) = 380*n^2 - 1532*n + 1224 for n>5.

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

G.f.: 4*x^2*(2 + 66*x + 104*x^2 + 43*x^3 - 15*x^4 - 5*x^5 - 5*x^6) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>8.

(End)

Example

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

Crossrefs

Cf. A187286.

Sequence in context: A348122 A060355 A060859 * A187191 A054607 A254408

Adjacent sequences: A187286 A187287 A187288 * A187290 A187291 A187292

Keyword

nonn

Author

R. H. Hardin, Mar 08 2011

Status

approved