T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1 or 3 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) =33a(12) =41a(13) =33a(14) =6a(15) =9a(16) =104a(17) =120a(18) =120a(19) =104a(20) =9a(21) =13a(22) =228a(23) =465a(24) =534a(25) =465a(26) =228a(27) =13a(28) =19a(29) =529