1/9 the number of (n+1) X 8 0..2 arrays with all 2 X 2 subblocks having the same four values.

Terms

a(0) =289a(1) =295a(2) =305a(3) =325a(4) =361a(5) =433a(6) =569a(7) =841a(8) =1369a(9) =2425a(10) =4505a(11) =8665a(12) =16921a(13) =33433a(14) =66329a(15) =132121a(16) =263449a(17) =526105a(18) =1050905a(19) =2100505a(20) =4198681a(21) =8395033a(22) =16785689a(23) =33567001a(24) =67125529a(25) =134242585a(26) =268468505a(27) =536920345a(28) =1073807641a(29) =2147582233