T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 3 or 4 king-move neighboring 1s.

Terms

a(0) =1a(1) =2a(2) =2a(3) =3a(4) =8a(5) =3a(6) =4a(7) =15a(8) =15a(9) =4a(10) =6a(11) =41a(12) =47a(13) =41a(14) =6a(15) =9a(16) =122a(17) =164a(18) =164a(19) =122a(20) =9a(21) =13a(22) =308a(23) =694a(24) =1011a(25) =694a(26) =308a(27) =13a(28) =19a(29) =855