1/16 the number of (n+1) X 4 0..3 arrays with all 2 X 2 subblocks having the same four values.

Terms

a(0) =49a(1) =61a(2) =82a(3) =124a(4) =202a(5) =358a(6) =658a(7) =1258a(8) =2434a(9) =4786a(10) =9442a(11) =18754a(12) =37282a(13) =74338a(14) =148258a(15) =296098a(16) =591394a(17) =1181986a(18) =2362402a(19) =4723234a(20) =9443362a(21) =18883618a(22) =37761058a(23) =75515938a(24) =151019554a(25) =302026786a(26) =604028962a(27) =1208033314a(28) =2416017442a(29) =4831985698