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A198717 Number of n X 2 0..6 arrays with values 0..6 introduced in row major order and no element equal to any horizontal or vertical neighbor.

%I A198717 #8 Feb 22 2018 16:29:15
%S A198717 1,4,34,499,10507,272410,7817980,234638905,7176366133,221220625936,
%T A198717 6841771033846,211886983790431,6565800345745279,203504808219690982,
%U A198717 6308194354577750032,195548116214389189477,6061914804816147034345
%N A198717 Number of n X 2 0..6 arrays with values 0..6 introduced in row major order and no element equal to any horizontal or vertical neighbor.
%C A198717 Column 2 of A198723.
%H A198717 R. H. Hardin, <a href="/A198717/b198717.txt">Table of n, a(n) for n = 1..200</a>
%F A198717 Empirical: a(n) = 55*a(n-1) - 918*a(n-2) + 5818*a(n-3) - 13417*a(n-4) + 8463*a(n-5).
%F A198717 Conjectures from _Colin Barker_, Feb 22 2018: (Start)
%F A198717 G.f.: x*(1 - 51*x + 732*x^2 - 3517*x^3 + 4419*x^4) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 13*x)*(1 - 31*x)).
%F A198717 a(n) = 11/30 + 3^n/8 + 7^(n-1)/6 + 13^(n-1)/12 + 31^(n-1)/120.
%F A198717 (End)
%e A198717 Some solutions with all values 0 to 6 for n=4:
%e A198717 ..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
%e A198717 ..2..3....2..3....2..3....2..3....2..3....2..3....2..0....2..3....2..3....2..3
%e A198717 ..4..5....4..5....4..5....4..5....4..1....4..5....3..4....4..5....4..0....1..4
%e A198717 ..6..1....6..0....2..6....6..2....5..6....6..4....5..6....0..6....5..6....5..6
%Y A198717 Cf. A198723.
%K A198717 nonn
%O A198717 1,2
%A A198717 _R. H. Hardin_, Oct 29 2011