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

Terms

a(0) =2a(1) =4a(2) =4a(3) =7a(4) =11a(5) =7a(6) =13a(7) =33a(8) =33a(9) =13a(10) =24a(11) =98a(12) =164a(13) =98a(14) =24a(15) =44a(16) =291a(17) =811a(18) =811a(19) =291a(20) =44a(21) =81a(22) =865a(23) =4035a(24) =6659a(25) =4035a(26) =865a(27) =81a(28) =149a(29) =2570