A187051 - OEIS

%I #10 Apr 20 2018 08:12:49

%S 0,0,0,400,14024,86608,285048,668176,1272720,2110944,3180724,4475176,

%T 5989600,7722744,9674608,11845192,14234496,16842520,19669264,22714728,

%U 25978912,29461816,33163440,37083784,41222848,45580632,50157136,54952360

%N Number of 7-step one or two space at a time bishop's tours on an n X n board summed over all starting positions.

%C Row 7 of A187046.

%H R. H. Hardin, <a href="/A187051/b187051.txt">Table of n, a(n) for n = 1..35</a>

%F Empirical: a(n) = 109360*n^2 - 1219576*n + 3362248 for n>11.

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

%F G.f.: 4*x^4*(100 + 3206*x + 11434*x^2 + 16724*x^3 + 14708*x^4 + 9182*x^5 + 3066*x^6 - 531*x^7 - 1721*x^8 - 1175*x^9 - 313*x^10) / (1 - x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>14.

%F (End)

%e Some solutions for 4 X 4:

%e ..0..1..0..3....0..2..0..0....0..2..0..7....0..3..0..7....0..7..0..0

%e ..5..0..2..0....3..0..6..0....3..0..6..0....2..0..5..0....3..0..6..0

%e ..0..4..0..7....0..5..0..1....0..5..0..1....0..6..0..4....0..4..0..1

%e ..0..0..6..0....7..0..4..0....0..0..4..0....0..0..1..0....5..0..2..0

%Y Cf. A187046.

%K nonn

%O 1,4

%A _R. H. Hardin_, Mar 02 2011