Number of n X 2 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 3 1s.

Terms

a(0) =2a(1) =5a(2) =11a(3) =24a(4) =55a(5) =123a(6) =276a(7) =621a(8) =1395a(9) =3134a(10) =7043a(11) =15825a(12) =35558a(13) =79899a(14) =179531a(15) =403402a(16) =906437a(17) =2036745a(18) =4576524a(19) =10283357a(20) =23106493a(21) =51919818a(22) =116662773a(23) =262138871a(24) =589020696a(25) =1323517491a(26) =2973916807a(27) =6682330408a(28) =15015060133a(29) =33738533867