Number of n X 2 0..1 arrays with each 1 adjacent to 3 or 4 king-move neighboring 1s.

Terms

a(0) =1a(1) =2a(2) =3a(3) =4a(4) =8a(5) =17a(6) =31a(7) =71a(8) =166a(9) =365a(10) =856a(11) =2020a(12) =4675a(13) =10985a(14) =25869a(15) =60578a(16) =142347a(17) =334748a(18) =785984a(19) =1846905a(20) =4340975a(21) =10198815a(22) =23965446a(23) =56319245a(24) =132336896a(25) =310971516a(26) =730753851a(27) =1717154937a(28) =4035069173a(29) =9481906914