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

Terms

a(0) =1a(1) =2a(2) =2a(3) =3a(4) =5a(5) =3a(6) =4a(7) =11a(8) =11a(9) =4a(10) =6a(11) =24a(12) =33a(13) =24a(14) =6a(15) =9a(16) =55a(17) =114a(18) =114a(19) =55a(20) =9a(21) =13a(22) =123a(23) =377a(24) =578a(25) =377a(26) =123a(27) =13a(28) =19a(29) =276