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Number of n X 2 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
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%I #9 Feb 11 2019 06:59:34

%S 1,3,24,232,2232,20880,190656,1707264,15046272,130854656,1125285888,

%T 9583835136,80941029376,678574706688,5651894845440,46802046418944,

%U 385539453517824,3161014415327232,25806384396763136,209862489033670656

%N Number of n X 2 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A279651/b279651.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 24*a(n-1) - 204*a(n-2) + 704*a(n-3) - 816*a(n-4) + 384*a(n-5) - 64*a(n-6) for n>7.

%F Empirical g.f.: x*(1 - 21*x + 156*x^2 - 436*x^3 + 264*x^4 - 192*x^5 + 32*x^6) / (1 - 8*x + 4*x^2)^3. - _Colin Barker_, Feb 11 2019

%e Some solutions for n=4:

%e ..0..0. .0..0. .0..0. .0..1. .0..1. .0..1. .0..1. .0..1. .0..0. .0..0

%e ..0..1. .0..1. .1..2. .1..1. .1..0. .2..2. .1..2. .1..0. .0..1. .1..1

%e ..2..1. .0..1. .1..1. .1..0. .0..0. .2..2. .2..2. .0..0. .0..2. .1..2

%e ..0..1. .2..0. .1..2. .1..2. .2..2. .1..2. .2..0. .1..1. .2..0. .0..2

%Y Column 2 of A279657.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 16 2016