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%I #19 Dec 21 2019 15:26:43
%S 0,2,4,6,10,18,32,56,98,172,302,530,930,1632,2864,5026,8820,15478,
%T 27162,47666,83648,146792,257602,452060,793310,1392162,2443074,
%U 4287296,7523680,13203138,23169892,40660326,71353898,125217362,219741152,385618840
%N Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal.
%C Column 1 of A232589.
%H R. H. Hardin, <a href="/A232582/b232582.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) - a(n-2) + a(n-3) = 2*A005314(n-1).
%F Empirical: G.f.: -2*x^2 / ( -1+2*x-x^2+x^3 ). - _R. J. Mathar_, Nov 23 2014
%F Theorem: a(n) = Sum_{j=1..floor((n-2)/3)} 2* Hypergeometric2F1([2+3*j-n,-(2j+1)], [1], 1). - _Richard Turk_, Oct 22 2019
%e Some solutions for n=7:
%e 2 1 0 1 2 1 0 1 0 1 0 1 0 1 2 1 0 1 2 1
%e 0 1 2 1 0 1 2 0 2 1 2 0 2 1 0 2 2 0 0 1
%e 2 0 0 1 2 0 1 2 0 2 1 2 0 1 1 0 1 2 2 0
%e 1 2 2 1 1 2 1 0 1 0 0 1 2 0 1 2 0 1 1 2
%e 1 0 0 1 0 1 2 1 2 1 2 0 1 2 1 0 2 1 1 0
%e 1 2 2 0 2 1 0 2 0 1 1 2 0 1 1 2 0 2 2 1
%e 1 0 1 2 0 2 1 0 2 0 1 0 2 0 1 0 1 0 0 2
%e 1 2 1 0 1 0 1 2 1 2 1 2 1 2 1 2 1 2 1 0
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 26 2013