T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 2 or 4 king-move neighboring 1s.

Terms

a(0) =2a(1) =3a(2) =3a(3) =5a(4) =9a(5) =5a(6) =8a(7) =21a(8) =21a(9) =8a(10) =13a(11) =57a(12) =69a(13) =57a(14) =13a(15) =21a(16) =153a(17) =258a(18) =258a(19) =153a(20) =21a(21) =34a(22) =393a(23) =963a(24) =1463a(25) =963a(26) =393a(27) =34a(28) =55a(29) =1041