A187029 Number of 4-step one or two collinear space at a time queen's tours on an n X n board summed over all starting positions.

0, 24, 1344, 7056, 19568, 39348, 66360, 100380, 141408, 189444, 244488, 306540, 375600, 451668, 534744, 624828, 721920, 826020, 937128, 1055244, 1180368, 1312500, 1451640, 1597788, 1750944, 1911108, 2078280, 2252460, 2433648, 2621844

Offset

1,2

Comments

Row 4 of A187027.

Links

R. H. Hardin, Table of n, a(n) for n = 1..31

Formula

Empirical: a(n) = 3504*n^2 - 18540*n + 24444 for n>5.

Conjectures from Colin Barker, Apr 20 2018: (Start)

G.f.: 4*x^2*(6 + 318*x + 774*x^2 + 602*x^3 + 117*x^4 - 9*x^5 - 56*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..0..0..0....2..0..3..4....0..0..0..4....0..0..0..0....0..2..0..0
..0..0..0..1....0..1..0..0....1..2..3..0....2..3..0..0....4..1..3..0
..0..0..3..4....0..0..0..0....0..0..0..0....1..0..0..0....0..0..0..0
..0..0..0..2....0..0..0..0....0..0..0..0....0..4..0..0....0..0..0..0

Crossrefs

Cf. A187027.

Sequence in context: A074652 A367706 A188807 * A186967 A068294 A003170

Adjacent sequences: A187026 A187027 A187028 * A187030 A187031 A187032

Keyword

nonn

Author

R. H. Hardin, Mar 02 2011

Status

approved