1/9 the number of (n+1) X 3 0..2 arrays with all 2 X 2 subblocks having the same four values.

Terms

a(0) =15a(1) =21a(2) =31a(3) =51a(4) =87a(5) =159a(6) =295a(7) =567a(8) =1095a(9) =2151a(10) =4231a(11) =8391a(12) =16647a(13) =33159a(14) =66055a(15) =131847a(16) =263175a(17) =525831a(18) =1050631a(19) =2100231a(20) =4198407a(21) =8394759a(22) =16785415a(23) =33566727a(24) =67125255a(25) =134242311a(26) =268468231a(27) =536920071a(28) =1073807367a(29) =2147581959