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

Terms

a(0) =1a(1) =2a(2) =2a(3) =4a(4) =11a(5) =4a(6) =7a(7) =29a(8) =29a(9) =7a(10) =12a(11) =80a(12) =104a(13) =80a(14) =12a(15) =21a(16) =261a(17) =467a(18) =467a(19) =261a(20) =21a(21) =37a(22) =789a(23) =2197a(24) =3472a(25) =2197a(26) =789a(27) =37a(28) =65a(29) =2354