T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2 or 3 1s.

Terms

a(0) =2a(1) =3a(2) =3a(3) =5a(4) =8a(5) =5a(6) =8a(7) =20a(8) =20a(9) =8a(10) =13a(11) =51a(12) =76a(13) =51a(14) =13a(15) =21a(16) =132a(17) =299a(18) =299a(19) =132a(20) =21a(21) =34a(22) =341a(23) =1198a(24) =1877a(25) =1198a(26) =341a(27) =34a(28) =55a(29) =883