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

%I #7 Oct 22 2018 10:55:07

%S 344,2064,12600,78420,477144,2908188,17766000,110572200,672773040,

%T 4100545080,25050060000,155906802000,948609986400,5781768562800,

%U 35320584600000,219828590820000,1337540080824000,8152293673548000

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

%H R. H. Hardin, <a href="/A237243/b237243.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 1410*a(n-4) for n>6.

%F Empirical g.f.: 4*x*(86 + 516*x + 3150*x^2 + 19605*x^3 - 1974*x^4 - 513*x^5) / (1 - 1410*x^4). - _Colin Barker_, Oct 22 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 2 of A237249.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 05 2014