T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 3 or 5 king-move neighboring 1s.

Terms

a(0) =2a(1) =3a(2) =3a(3) =5a(4) =6a(5) =5a(6) =8a(7) =14a(8) =14a(9) =8a(10) =13a(11) =31a(12) =43a(13) =31a(14) =13a(15) =21a(16) =70a(17) =132a(18) =132a(19) =70a(20) =21a(21) =34a(22) =157a(23) =402a(24) =573a(25) =402a(26) =157a(27) =34a(28) =55a(29) =353