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%I #9 Oct 22 2018 01:37:53
%S 268,984,3284,10888,36180,120540,401520,1336540,4448892,14811704,
%T 49313092,164172108,546554288,1819586828,6057775468,20167512408,
%U 67141506132,223527096380,744165226864,2477470556540,8247979825436
%N Number of (n+1) X (2+1) 0..2 arrays with the maximum plus the minimum of every 2 X 2 subblock differing from its horizontal and vertical neighbors by exactly one.
%H R. H. Hardin, <a href="/A237228/b237228.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 4*a(n-2) + 5*a(n-3) + 21*a(n-4) + 12*a(n-5) + 4*a(n-6) for n>8.
%F Empirical g.f.: 4*x*(67 + 179*x + 307*x^2 + 582*x^3 + 402*x^4 + 127*x^5 - 6*x^6 - 8*x^7) / (1 - x - 4*x^2 - 5*x^3 - 21*x^4 - 12*x^5 - 4*x^6). - _Colin Barker_, Oct 21 2018
%e Some solutions for n=5:
%e ..0..0..0....1..0..1....2..2..1....1..2..1....1..1..0....2..0..1....0..2..1
%e ..0..1..2....1..1..2....0..1..2....2..1..0....1..2..2....1..0..0....0..1..1
%e ..2..2..1....1..1..2....0..1..0....0..0..0....0..1..2....0..1..2....0..1..1
%e ..2..1..0....1..0..0....2..1..1....1..1..2....0..0..0....1..2..1....2..2..1
%e ..1..0..1....2..1..1....2..1..1....1..1..2....0..0..1....1..1..0....1..1..0
%e ..1..0..2....1..1..1....0..0..1....0..1..0....0..1..2....1..1..0....1..1..1
%Y Column 2 of A237234.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 05 2014