1/9 the number of (n+1) X 4 0..2 arrays with all 2 X 2 subblocks having the same four values.

Terms

a(0) =25a(1) =31a(2) =41a(3) =61a(4) =97a(5) =169a(6) =305a(7) =577a(8) =1105a(9) =2161a(10) =4241a(11) =8401a(12) =16657a(13) =33169a(14) =66065a(15) =131857a(16) =263185a(17) =525841a(18) =1050641a(19) =2100241a(20) =4198417a(21) =8394769a(22) =16785425a(23) =33566737a(24) =67125265a(25) =134242321a(26) =268468241a(27) =536920081a(28) =1073807377a(29) =2147581969