A187050 - OEIS

%I #11 Apr 20 2018 10:05:16

%S 0,0,0,584,6952,29500,79088,162320,281320,435436,623508,845084,

%T 1100164,1388748,1710836,2066428,2455524,2878124,3334228,3823836,

%U 4346948,4903564,5493684,6117308,6774436,7465068,8189204,8946844,9737988,10562636

%N Number of 6-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.

%C Row 6 of A187046.

%H R. H. Hardin, <a href="/A187050/b187050.txt">Table of n, a(n) for n = 1..35</a>

%F Empirical: a(n) = 16752*n^2 - 163720*n + 397436 for n>9.

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

%F G.f.: 4*x^3*(146 + 1300*x + 2599*x^2 + 2715*x^3 + 1651*x^4 + 531*x^5 - 163*x^6 - 290*x^7 - 113*x^8) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>12.

%F (End)

%e Some solutions for 4 X 4:

%e ..0..0..0..0....0..4..0..0....3..0..5..0....3..0..1..0....0..0..4..0

%e ..0..5..0..3....5..0..3..0....0..4..0..1....0..2..0..5....0..5..0..1

%e ..1..0..4..0....0..6..0..2....6..0..2..0....0..0..4..0....3..0..6..0

%e ..0..2..0..6....0..0..1..0....0..0..0..0....0..6..0..0....0..2..0..0

%Y Cf. A187046.

%K nonn

%O 1,4

%A _R. H. Hardin_, Mar 02 2011