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Number of (n+1)X(2+1) 0..3 arrays with the upper median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one
1

%I #4 Feb 16 2014 06:49:42

%S 1494,10014,59014,357672,2270776,14222512,88114176,550642732,

%T 3451069630,21560822458,134629301012,841895591970,5264528244482,

%U 32900378176060,205627745431856,1285545369352008,8036253217579508,50230256232200120

%N Number of (n+1)X(2+1) 0..3 arrays with the upper median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one

%C Column 2 of A237974

%H R. H. Hardin, <a href="/A237968/b237968.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 84*a(n-3) +773*a(n-4) +1372*a(n-5) +3600*a(n-6) -8931*a(n-7) -55854*a(n-8) -94782*a(n-9) -31846*a(n-10) +191731*a(n-11) +369506*a(n-12) +355656*a(n-13) +149556*a(n-14) +448480*a(n-15) +642040*a(n-16) +99840*a(n-17) for n>20

%e Some solutions for n=3

%e ..2..1..0....1..1..0....0..3..0....0..2..1....3..1..2....3..2..0....1..1..0

%e ..1..2..1....1..3..2....1..2..3....1..0..3....0..1..2....2..3..1....2..3..1

%e ..1..1..2....0..2..3....0..1..0....2..3..2....0..0..0....0..1..1....3..0..2

%e ..2..3..3....0..1..0....2..3..1....3..1..1....3..1..0....1..2..2....2..1..0

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 16 2014