Half the number of (n+1) X 2 binary arrays with no 2X2 subblock having exactly 2 ones.

Terms

a(0) =2a(1) =5a(2) =13a(3) =33a(4) =85a(5) =217a(6) =557a(7) =1425a(8) =3653a(9) =9353a(10) =23965a(11) =61377a(12) =157237a(13) =402745a(14) =1031693a(15) =2642673a(16) =6769445a(17) =17340137a(18) =44417917a(19) =113778465a(20) =291450133a(21) =746563993a(22) =1912364525a(23) =4898620497a(24) =12548078597a(25) =32142560585a(26) =82334874973a(27) =210905117313a(28) =540244617205