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Number of (n+1)X(1+1) 0..2 arrays with every element both >= and <= some horizontal or vertical neighbor
2

%I #5 Nov 19 2013 04:29:35

%S 15,109,611,3635,21717,129323,770747,4593729,27378111,163172235,

%T 972498865,5796045587,34544152883,205881488613,1227043758875,

%U 7313121735911,43585853505657,259769588739759,1548214244035995

%N Number of (n+1)X(1+1) 0..2 arrays with every element both >= and <= some horizontal or vertical neighbor

%C Column 1 of A232124

%H R. H. Hardin, <a href="/A232117/b232117.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +4*a(n-2) +12*a(n-3) -7*a(n-4) -14*a(n-5) -33*a(n-6) -22*a(n-7) +4*a(n-8) +4*a(n-9)

%e Some solutions for n=6

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

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 19 2013