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Number of (n+1) X (n+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 23 2018 11:56:40

%S 81,636,1310,2012,4622,9368,18344,44292,102536,211268,402152,1015572,

%T 2337608,4914788,9150632,23921652,54827528,116999108,214315112,

%U 574558932,1312885448,2831048228,5126666792,13988255412,31897292168,69273334148

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

%H R. H. Hardin, <a href="/A237629/b237629.txt">Table of n, a(n) for n = 1..36</a>

%F Empirical: a(n) = 4*a(n-2) + 25*a(n-4) - 100*a(n-6) for n>11.

%F Empirical g.f.: x*(81 + 636*x + 986*x^2 - 532*x^3 - 2643*x^4 - 14580*x^5 - 24794*x^6 + 20120*x^7 + 44610*x^8 + 1100*x^9 - 4392*x^10) / ((1 - 2*x)*(1 + 2*x)*(1 - 5*x^2)*(1 + 5*x^2)). - _Colin Barker_, Oct 23 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Diagonal of A237637.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 10 2014