T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 3 king-move neighboring 1s.

Terms

a(0) =2a(1) =4a(2) =4a(3) =8a(4) =15a(5) =8a(6) =16a(7) =45a(8) =45a(9) =16a(10) =32a(11) =152a(12) =228a(13) =152a(14) =32a(15) =64a(16) =511a(17) =1256a(18) =1256a(19) =511a(20) =64a(21) =128a(22) =1681a(23) =6859a(24) =11925a(25) =6859a(26) =1681a(27) =128a(28) =256a(29) =5588