T(n,k)=Half the number of (n+2)X(k+2) binary arrays with each 3X3 subblock having sum 4 or 5.

Terms

a(0) =126a(1) =606a(2) =606a(3) =2904a(4) =3988a(5) =2904a(6) =14229a(7) =25808a(8) =25808a(9) =14229a(10) =70767a(11) =173121a(12) =222632a(13) =173121a(14) =70767a(15) =351549a(16) =1190637a(17) =2009622a(18) =2009622a(19) =1190637a(20) =351549a(21) =1750896a(22) =8178097a(23) =18829218a(24) =24581099a(25) =18829218a(26) =8178097a(27) =1750896a(28) =8730234a(29) =56422648