A198662 Number of nX1 0..4 arrays with values 0..4 introduced in row major order and each element equal to one or two horizontal and vertical neighbors

0, 1, 1, 2, 3, 6, 11, 23, 47, 103, 226, 517, 1194, 2830, 6778, 16498, 40501, 100420, 250513, 628749, 1584525, 4007957, 10164528, 25835883, 65777232, 167694004, 427960360, 1093068944, 2793604179, 7143313914, 18272673575, 46755936515