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%I #9 Feb 14 2019 07:44:27
%S 4,59,858,12484,181640,2642832,38452768,559481408,8140361856,
%T 118440917248,1723295736320,25073667646464,364817712941056,
%U 5308037322346496,77231064216379392,1123699197608083456
%N Number of n X 3 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
%H R. H. Hardin, <a href="/A280668/b280668.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 14*a(n-1) + 8*a(n-2).
%F Conjectures from _Colin Barker_, Feb 14 2019: (Start)
%F G.f.: x*(4 + 3*x) / (1 - 14*x - 8*x^2).
%F a(n) = ((7-sqrt(57))^n*(-11+3*sqrt(57)) + (7+sqrt(57))^n*(11+3*sqrt(57))) / (16*sqrt(57)).
%F (End)
%e Some solutions for n=4:
%e ..0..1..1. .0..1..1. .0..1..0. .0..1..2. .0..0..1. .0..1..0. .0..1..0
%e ..0..2..2. .0..2..1. .0..2..0. .1..0..1. .1..2..2. .1..2..0. .1..2..1
%e ..0..1..0. .0..1..2. .0..1..1. .1..0..2. .1..0..1. .1..1..2. .2..0..2
%e ..1..2..2. .0..1..1. .0..0..1. .2..1..2. .2..2..1. .0..2..0. .0..2..1
%Y Column 3 of A280673.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 07 2017
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