A069448 Half the number of 3 X n binary arrays with no path of adjacent 1's or adjacent 0's from top to bottom or side to side.
3, 35, 269, 1723, 10123, 56757, 309755, 1663515, 8846821, 46767491, 246319875, 1294402053, 6792548971, 35614277883, 186632524741, 977711862035, 5120933346419
Offset: 2