1/16 the number of (n+1) X 9 0..3 arrays with all 2 X 2 subblocks having the same four values.

Terms

a(0) =1225a(1) =1237a(2) =1258a(3) =1300a(4) =1378a(5) =1534a(6) =1834a(7) =2434a(8) =3610a(9) =5962a(10) =10618a(11) =19930a(12) =38458a(13) =75514a(14) =149434a(15) =297274a(16) =592570a(17) =1183162a(18) =2363578a(19) =4724410a(20) =9444538a(21) =18884794a(22) =37762234a(23) =75517114a(24) =151020730a(25) =302027962a(26) =604030138a(27) =1208034490a(28) =2416018618