1/9 the number of (n+1) X 7 0..2 arrays with all 2 X 2 subblocks having the same four values.

Terms

a(0) =153a(1) =159a(2) =169a(3) =189a(4) =225a(5) =297a(6) =433a(7) =705a(8) =1233a(9) =2289a(10) =4369a(11) =8529a(12) =16785a(13) =33297a(14) =66193a(15) =131985a(16) =263313a(17) =525969a(18) =1050769a(19) =2100369a(20) =4198545a(21) =8394897a(22) =16785553a(23) =33566865a(24) =67125393a(25) =134242449a(26) =268468369a(27) =536920209a(28) =1073807505a(29) =2147582097