A187029 - OEIS

%I #10 Apr 20 2018 06:08:47

%S 0,24,1344,7056,19568,39348,66360,100380,141408,189444,244488,306540,

%T 375600,451668,534744,624828,721920,826020,937128,1055244,1180368,

%U 1312500,1451640,1597788,1750944,1911108,2078280,2252460,2433648,2621844

%N 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.

%C Row 4 of A187027.

%H R. H. Hardin, <a href="/A187029/b187029.txt">Table of n, a(n) for n = 1..31</a>

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

%F Conjectures from _Colin Barker_, Apr 20 2018: (Start)

%F 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.

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

%F (End)

%e Some solutions for 4 X 4:

%e ..0..0..0..0....2..0..3..4....0..0..0..4....0..0..0..0....0..2..0..0

%e ..0..0..0..1....0..1..0..0....1..2..3..0....2..3..0..0....4..1..3..0

%e ..0..0..3..4....0..0..0..0....0..0..0..0....1..0..0..0....0..0..0..0

%e ..0..0..0..2....0..0..0..0....0..0..0..0....0..4..0..0....0..0..0..0

%Y Cf. A187027.

%K nonn

%O 1,2

%A _R. H. Hardin_, Mar 02 2011