T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 4 king-move neighboring 1s.

Terms

a(0) =2a(1) =4a(2) =4a(3) =8a(4) =16a(5) =8a(6) =16a(7) =58a(8) =58a(9) =16a(10) =32a(11) =216a(12) =351a(13) =216a(14) =32a(15) =64a(16) =808a(17) =2258a(18) =2258a(19) =808a(20) =64a(21) =128a(22) =3016a(23) =14566a(24) =26278a(25) =14566a(26) =3016a(27) =128a(28) =256a(29) =11264