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

Terms

a(0) =2a(1) =8a(2) =15a(3) =33a(4) =104a(5) =228a(6) =529a(7) =1469a(8) =3442a(9) =8212a(10) =21431a(11) =51717a(12) =125296a(13) =317400a(14) =775809a(15) =1895433a(16) =4734066a(17) =11634128a(18) =28553071a(19) =70839225a(20) =174478216a(21) =429240572a(22) =1061586753a(23) =2617025573a(24) =6446295426a(25) =15919369724a(26) =39257673143a(27) =96762290109