T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 2 or 3 king-move neighboring 1s.

Terms

a(0) =2a(1) =3a(2) =3a(3) =5a(4) =10a(5) =5a(6) =8a(7) =25a(8) =25a(9) =8a(10) =13a(11) =68a(12) =82a(13) =68a(14) =13a(15) =21a(16) =208a(17) =334a(18) =334a(19) =208a(20) =21a(21) =34a(22) =609a(23) =1451a(24) =2295a(25) =1451a(26) =609a(27) =34a(28) =55a(29) =1785