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

Terms

a(0) =561a(1) =567a(2) =577a(3) =597a(4) =633a(5) =705a(6) =841a(7) =1113a(8) =1641a(9) =2697a(10) =4777a(11) =8937a(12) =17193a(13) =33705a(14) =66601a(15) =132393a(16) =263721a(17) =526377a(18) =1051177a(19) =2100777a(20) =4198953a(21) =8395305a(22) =16785961a(23) =33567273a(24) =67125801a(25) =134242857a(26) =268468777a(27) =536920617a(28) =1073807913a(29) =2147582505