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Number of (n+1) X (2+1) 0..2 arrays with the upper median of every 2 X 2 subblock differing from its horizontal and vertical neighbors by exactly one.

1

`%I #8 Oct 24 2018 06:02:35
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`%S 260,636,1220,2356,4500,8594,16448,31672,60362,116180,223768,429680,
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`%T 822032,1584164,3047968,5848520,11216480,21603248,41526472,79692176,
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`%U 153032384,294531296,565871200,1086330032,2087379872,4014989408
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`%N Number of (n+1) X (2+1) 0..2 arrays with the upper median of every 2 X 2 subblock differing from its horizontal and vertical neighbors by exactly one.
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`%H R. H. Hardin, <a href="/A237631/b237631.txt">Table of n, a(n) for n = 1..210</a>
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`%F Empirical: a(n) = 3*a(n-3) + 10*a(n-4) - 12*a(n-7) - 6*a(n-8) for n>12.
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`%F Empirical g.f.: 2*x*(130 + 318*x + 610*x^2 + 788*x^3 - 4*x^4 - 713*x^5 - 1410*x^6 - 1134*x^7 - 614*x^8 - 324*x^9 - 68*x^10 + 5*x^11) / (1 - 3*x^3 - 10*x^4 + 12*x^7 + 6*x^8). - _Colin Barker_, Oct 24 2018
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`%e Some solutions for n=5:
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`%e ..2..1..1....1..1..2....0..1..0....2..0..1....2..2..1....0..1..1....0..1..2
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`%e ..0..2..1....0..2..1....2..0..0....2..1..0....1..0..0....0..0..2....1..2..1
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`%e ..0..1..2....2..1..0....2..1..2....0..0..0....2..1..0....1..2..1....2..0..0
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`%e ..0..0..0....0..0..0....0..0..2....0..1..2....1..2..0....2..1..0....1..0..1
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`%e ..2..1..0....0..1..2....1..0..1....1..2..1....0..1..2....0..0..0....0..0..2
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`%e ..2..0..2....0..2..1....1..2..2....2..1..1....0..0..0....0..1..2....1..2..0
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`%Y Column 2 of A237637.
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`%K nonn
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`%O 1,1
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`%A _R. H. Hardin_, Feb 10 2014
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