T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

Terms

a(0) =1a(1) =2a(2) =2a(3) =4a(4) =10a(5) =4a(6) =7a(7) =29a(8) =29a(9) =7a(10) =12a(11) =87a(12) =147a(13) =87a(14) =12a(15) =21a(16) =280a(17) =774a(18) =774a(19) =280a(20) =21a(21) =37a(22) =876a(23) =4080a(24) =7071a(25) =4080a(26) =876a(27) =37a(28) =65a(29) =2735