T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.

Terms

a(0) =1a(1) =2a(2) =2a(3) =4a(4) =10a(5) =4a(6) =7a(7) =36a(8) =36a(9) =7a(10) =12a(11) =126a(12) =234a(13) =126a(14) =12a(15) =21a(16) =454a(17) =1534a(18) =1534a(19) =454a(20) =21a(21) =37a(22) =1632a(23) =10291a(24) =19026a(25) =10291a(26) =1632a(27) =37a(28) =65a(29) =5854