T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 4 1s.

Terms

a(0) =2a(1) =3a(2) =3a(3) =5a(4) =8a(5) =5a(6) =8a(7) =19a(8) =19a(9) =8a(10) =13a(11) =48a(12) =74a(13) =48a(14) =13a(15) =21a(16) =120a(17) =278a(18) =278a(19) =120a(20) =21a(21) =34a(22) =299a(23) =1067a(24) =1634a(25) =1067a(26) =299a(27) =34a(28) =55a(29) =747