T(n,k)=Number of n X k 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1s.

Terms

a(0) =2a(1) =3a(2) =3a(3) =5a(4) =6a(5) =5a(6) =8a(7) =13a(8) =13a(9) =8a(10) =13a(11) =28a(12) =39a(13) =28a(14) =13a(15) =21a(16) =60a(17) =115a(18) =115a(19) =60a(20) =21a(21) =34a(22) =129a(23) =337a(24) =467a(25) =337a(26) =129a(27) =34a(28) =55a(29) =277