A241350 Number of n X n 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.
2, 3, 19, 128, 615, 35880, 1904754, 109041097
Offset: 1
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Some solutions for n=4 ..3..2..3..3....2..3..3..2....2..3..2..2....2..3..3..2....3..2..3..3 ..3..1..2..3....2..1..1..2....2..1..1..2....2..1..1..1....3..2..2..1 ..2..3..0..2....2..0..3..2....2..0..3..3....3..2..3..3....2..3..3..2 ..3..0..1..3....2..0..1..2....2..0..0..1....3..2..2..2....3..2..0..2
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