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Number of nX3 0..2 arrays avoiding the pattern z-2 z-1 z in any row or column
1

%I #5 Mar 31 2012 12:37:12

%S 26,676,15712,363465,8366690,192513201,4428597297,101873060353,

%T 2343406014665,53905733689480,1240001271788197,28523922980667486,

%U 656139776848417214,15093274671338487633,347192698846268632122

%N Number of nX3 0..2 arrays avoiding the pattern z-2 z-1 z in any row or column

%C Column 3 of A206700

%H R. H. Hardin, <a href="/A206695/b206695.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 29*a(n-1) -84*a(n-2) -1570*a(n-3) +6618*a(n-4) +28026*a(n-5) -136815*a(n-6) -145173*a(n-7) +1005714*a(n-8) -486446*a(n-9) -1842056*a(n-10) +1805556*a(n-11) +1069186*a(n-12) -1763040*a(n-13) +27675*a(n-14) +626313*a(n-15) -148782*a(n-16) -66294*a(n-17) +19454*a(n-18) +2708*a(n-19) -849*a(n-20) -37*a(n-21) +12*a(n-22)

%e Some solutions for n=4

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Feb 11 2012