T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 2 king-move neighboring 1s.

Terms

a(0) =2a(1) =4a(2) =4a(3) =7a(4) =12a(5) =7a(6) =13a(7) =30a(8) =30a(9) =13a(10) =24a(11) =96a(12) =136a(13) =96a(14) =24a(15) =44a(16) =286a(17) =687a(18) =687a(19) =286a(20) =44a(21) =81a(22) =848a(23) =3616a(24) =6784a(25) =3616a(26) =848a(27) =81a(28) =149a(29) =2620