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

Terms

a(0) =2a(1) =3a(2) =3a(3) =5a(4) =9a(5) =5a(6) =8a(7) =19a(8) =19a(9) =8a(10) =13a(11) =49a(12) =56a(13) =49a(14) =13a(15) =21a(16) =123a(17) =198a(18) =198a(19) =123a(20) =21a(21) =34a(22) =297a(23) =665a(24) =1059a(25) =665a(26) =297a(27) =34a(28) =55a(29) =739