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Number of (n+1)X(2+1) 0..2 arrays with no element equal to a strict majority of its horizontal, vertical, diagonal and diagonal neighbors, with values 0..2 introduced in row major order
1

%I #4 Nov 07 2013 06:23:52

%S 57,937,18334,352610,6781436,130633288,2516212586,48467679482,

%T 933608055112,17983615795542,346409439393284,6672714054969582,

%U 128533200257770904,2475871681865298784,47691495995570845668

%N Number of (n+1)X(2+1) 0..2 arrays with no element equal to a strict majority of its horizontal, vertical, diagonal and diagonal neighbors, with values 0..2 introduced in row major order

%C Column 2 of A231315

%H R. H. Hardin, <a href="/A231311/b231311.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 21*a(n-1) -26*a(n-2) -69*a(n-3) -1540*a(n-4) +1809*a(n-5) +1273*a(n-6) +5033*a(n-7) -10255*a(n-8) +22194*a(n-9) -27726*a(n-10) +2430*a(n-11) -43356*a(n-12) +163556*a(n-13) -127656*a(n-14) -74304*a(n-15) +140896*a(n-16) -51264*a(n-17)

%e Some solutions for n=3

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 07 2013