T(n,k)=Half the number of (n+1)X(k+1) binary arrays with no 2X2 subblock containing exactly one 1.

Terms

a(0) =6a(1) =19a(2) =19a(3) =60a(4) =104a(5) =60a(6) =190a(7) =561a(8) =561a(9) =190a(10) =602a(11) =3050a(12) =5074a(13) =3050a(14) =602a(15) =1908a(16) =16581a(17) =46514a(18) =46514a(19) =16581a(20) =1908a(21) =6048a(22) =90185a(23) =425802a(24) =723635a(25) =425802a(26) =90185a(27) =6048a(28) =19172a(29) =490546