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

Terms

a(0) =9a(1) =21a(2) =41a(3) =81a(4) =153a(5) =297a(6) =569a(7) =1113a(8) =2169a(9) =4281a(10) =8441a(11) =16761a(12) =33273a(13) =66297a(14) =132089a(15) =263673a(16) =526329a(17) =1051641a(18) =2101241a(19) =4200441a(20) =8396793a(21) =16789497a(22) =33570809a(23) =67133433a(24) =134250489a(25) =268484601a(26) =536936441a(27) =1073840121a(28) =2147614713a(29) =4295163897