A187298 Number of 3-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on an n X n board summed over all starting positions.

0, 2, 36, 98, 198, 330, 494, 690, 918, 1178, 1470, 1794, 2150, 2538, 2958, 3410, 3894, 4410, 4958, 5538, 6150, 6794, 7470, 8178, 8918, 9690, 10494, 11330, 12198, 13098, 14030, 14994, 15990, 17018, 18078, 19170, 20294, 21450, 22638, 23858, 25110, 26394

Offset

1,2

Comments

Row 3 of A187296.

Links

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

Formula

Empirical: a(n) = 16*n^2 - 44*n + 18 for n>3.

Conjectures from Colin Barker, Apr 23 2018: (Start)

G.f.: 2*x^2*(1 + 15*x - 2*x^2 + 5*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..1..0..0....0..0..0..0....0..0..0..0....0..0..1..0....0..0..0..3
..0..0..0..0....1..0..0..0....0..1..0..0....0..0..3..0....0..1..0..2
..3..2..0..0....0..0..0..0....0..3..0..0....0..0..2..0....0..0..0..0
..0..0..0..0....2..0..3..0....0..2..0..0....0..0..0..0....0..0..0..0

Crossrefs

Cf. A187296.

Sequence in context: A058517 A328963 A081310 * A069067 A278930 A258356

Adjacent sequences: A187295 A187296 A187297 * A187299 A187300 A187301

Keyword

nonn

Author

R. H. Hardin, Mar 08 2011

Status

approved