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

Terms

a(0) =2a(1) =4a(2) =4a(3) =7a(4) =12a(5) =7a(6) =13a(7) =29a(8) =29a(9) =13a(10) =24a(11) =85a(12) =111a(13) =85a(14) =24a(15) =44a(16) =248a(17) =468a(18) =468a(19) =248a(20) =44a(21) =81a(22) =664a(23) =1985a(24) =3159a(25) =1985a(26) =664a(27) =81a(28) =149a(29) =1897