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

Terms

a(0) =28a(1) =40a(2) =61a(3) =103a(4) =181a(5) =337a(6) =637a(7) =1237a(8) =2413a(9) =4765a(10) =9421a(11) =18733a(12) =37261a(13) =74317a(14) =148237a(15) =296077a(16) =591373a(17) =1181965a(18) =2362381a(19) =4723213a(20) =9443341a(21) =18883597a(22) =37761037a(23) =75515917a(24) =151019533a(25) =302026765a(26) =604028941a(27) =1208033293a(28) =2416017421a(29) =4831985677