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A280668 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.

%I A280668 #9 Feb 14 2019 07:44:27
%S A280668 4,59,858,12484,181640,2642832,38452768,559481408,8140361856,
%T A280668 118440917248,1723295736320,25073667646464,364817712941056,
%U A280668 5308037322346496,77231064216379392,1123699197608083456
%N A280668 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 A280668 R. H. Hardin, <a href="/A280668/b280668.txt">Table of n, a(n) for n = 1..210</a>
%F A280668 Empirical: a(n) = 14*a(n-1) + 8*a(n-2).
%F A280668 Conjectures from _Colin Barker_, Feb 14 2019: (Start)
%F A280668 G.f.: x*(4 + 3*x) / (1 - 14*x - 8*x^2).
%F A280668 a(n) = ((7-sqrt(57))^n*(-11+3*sqrt(57)) + (7+sqrt(57))^n*(11+3*sqrt(57))) / (16*sqrt(57)).
%F A280668 (End)
%e A280668 Some solutions for n=4:
%e A280668 ..0..1..1. .0..1..1. .0..1..0. .0..1..2. .0..0..1. .0..1..0. .0..1..0
%e A280668 ..0..2..2. .0..2..1. .0..2..0. .1..0..1. .1..2..2. .1..2..0. .1..2..1
%e A280668 ..0..1..0. .0..1..2. .0..1..1. .1..0..2. .1..0..1. .1..1..2. .2..0..2
%e A280668 ..1..2..2. .0..1..1. .0..0..1. .2..1..2. .2..2..1. .0..2..0. .0..2..1
%Y A280668 Column 3 of A280673.
%K A280668 nonn
%O A280668 1,1
%A A280668 _R. H. Hardin_, Jan 07 2017