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

Terms

a(0) =2a(1) =3a(2) =3a(3) =5a(4) =10a(5) =5a(6) =8a(7) =32a(8) =32a(9) =8a(10) =13a(11) =103a(12) =205a(13) =103a(14) =13a(15) =21a(16) =350a(17) =1292a(18) =1292a(19) =350a(20) =21a(21) =34a(22) =1201a(23) =8810a(24) =16059a(25) =8810a(26) =1201a(27) =34a(28) =55a(29) =4143