1/16 the number of (n+1) X 2 0..3 arrays with all 2 X 2 subblocks having the same four values.

Terms

a(0) =16a(1) =28a(2) =49a(3) =91a(4) =169a(5) =325a(6) =625a(7) =1225a(8) =2401a(9) =4753a(10) =9409a(11) =18721a(12) =37249a(13) =74305a(14) =148225a(15) =296065a(16) =591361a(17) =1181953a(18) =2362369a(19) =4723201a(20) =9443329a(21) =18883585a(22) =37761025a(23) =75515905a(24) =151019521a(25) =302026753a(26) =604028929a(27) =1208033281a(28) =2416017409a(29) =4831985665