T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having one or two 1s.

Terms

a(0) =10a(1) =28a(2) =28a(3) =78a(4) =116a(5) =78a(6) =220a(7) =474a(8) =474a(9) =220a(10) =618a(11) =1982a(12) =2804a(13) =1982a(14) =618a(15) =1740a(16) =8218a(17) =17216a(18) =17216a(19) =8218a(20) =1740a(21) =4894a(22) =34288a(23) =104058a(24) =157312a(25) =104058a(26) =34288a(27) =4894a(28) =13772a(29) =142600