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%I #8 Feb 13 2019 11:19:43
%S 2,6,66,554,4250,31242,223706,1571978,10887706,74545802,505624538,
%T 3402833418,22750442266,151248129802,1000625900506,6591782458762,
%U 43261686405658,282980475181450,1845507292321242,12003609559311114
%N Number of n X 3 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%H R. H. Hardin, <a href="/A280393/b280393.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 18*a(n-1) - 121*a(n-2) + 392*a(n-3) - 688*a(n-4) + 640*a(n-5) - 256*a(n-6) for n>7.
%F Empirical g.f.: 2*x*(1 - 2*x)*(1 - 13*x + 74*x^2 - 198*x^3 + 248*x^4 - 128*x^5) / (1 - 9*x + 20*x^2 - 16*x^3)^2. - _Colin Barker_, Feb 13 2019
%e Some solutions for n=4:
%e ..0..0..1. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0
%e ..0..1..1. .1..2..2. .1..1..1. .0..1..2. .1..1..1. .1..1..1. .1..1..1
%e ..0..0..1. .2..0..0. .0..1..1. .2..2..2. .2..1..1. .2..2..2. .1..1..0
%e ..0..0..0. .0..0..0. .1..1..1. .2..2..2. .1..1..1. .1..2..2. .1..1..1
%Y Column 3 of A280398.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 02 2017
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