A194534 Number of lower triangles of an n X n 0..2 array with new values introduced in row major order 0..2 and no element equal to more than one horizontal or vertical neighbor.
1, 4, 59, 1851, 119548, 16039294, 4460214471, 2572187445993, 3075932897564028, 7627704068111688574, 39223874584658826539499, 418261269510360187893175534, 9248796169262343437995449320699, 424095060368117191810477243815045914
Offset: 1
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Some solutions for 3X3 ..0......0......0......0......0......0......0......0......0......0......0 ..0.1....0.1....1.2....1.1....1.2....1.1....1.1....1.2....1.1....1.0....1.1 ..2.0.0..1.0.0..0.2.0..2.0.0..2.1.2..0.2.1..2.2.1..0.1.0..2.0.2..1.2.0..0.2.0
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