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

Author

R. H. Hardin, Mar 02 2011

Keywords

• nonn

Comments

Row 4 of A187027.

Examples

			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
		

Links

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

Crossrefs

Cf. A187027.

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)