T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1 or 4 king-move neighboring 1s.

Terms

a(0) =1a(1) =2a(2) =2a(3) =3a(4) =7a(5) =3a(6) =4a(7) =13a(8) =13a(9) =4a(10) =6a(11) =28a(12) =30a(13) =28a(14) =6a(15) =9a(16) =69a(17) =91a(18) =91a(19) =69a(20) =9a(21) =13a(22) =149a(23) =280a(24) =366a(25) =280a(26) =149a(27) =13a(28) =19a(29) =330