Number of n X 2 binary arrays with every 1 having exactly one king-move neighbor equal to 1.

Terms

a(0) =2a(1) =7a(2) =13a(3) =28a(4) =69a(5) =149a(6) =330a(7) =755a(8) =1681a(9) =3756a(10) =8457a(11) =18937a(12) =42418a(13) =95183a(14) =213349a(15) =478204a(16) =1072285a(17) =2403885a(18) =5388986a(19) =12082011a(20) =27086537a(21) =60724492a(22) =136139073a(23) =305209713a(24) =684246754a(25) =1534012759a(26) =3439098365a(27) =7710098140a(28) =17285247541a(29) =38751739141