1/9 the number of (n+1) X 6 0..2 arrays with all 2 X 2 subblocks having the same four values.

Terms

a(0) =81a(1) =87a(2) =97a(3) =117a(4) =153a(5) =225a(6) =361a(7) =633a(8) =1161a(9) =2217a(10) =4297a(11) =8457a(12) =16713a(13) =33225a(14) =66121a(15) =131913a(16) =263241a(17) =525897a(18) =1050697a(19) =2100297a(20) =4198473a(21) =8394825a(22) =16785481a(23) =33566793a(24) =67125321a(25) =134242377a(26) =268468297a(27) =536920137a(28) =1073807433a(29) =2147582025