1/16 the number of (n+1) X 8 0..3 arrays with all 2 X 2 subblocks having the same four values.

Terms

a(0) =625a(1) =637a(2) =658a(3) =700a(4) =778a(5) =934a(6) =1234a(7) =1834a(8) =3010a(9) =5362a(10) =10018a(11) =19330a(12) =37858a(13) =74914a(14) =148834a(15) =296674a(16) =591970a(17) =1182562a(18) =2362978a(19) =4723810a(20) =9443938a(21) =18884194a(22) =37761634a(23) =75516514a(24) =151020130a(25) =302027362a(26) =604029538a(27) =1208033890a(28) =2416018018a(29) =4831986274