T(n,k) = Number of n X k 0..1 arrays with each 1 adjacent to 1, 2 or 4 king-move neighboring 1's.

Terms

a(0) =1a(1) =2a(2) =2a(3) =4a(4) =11a(5) =4a(6) =7a(7) =31a(8) =31a(9) =7a(10) =12a(11) =88a(12) =126a(13) =88a(14) =12a(15) =21a(16) =287a(17) =575a(18) =575a(19) =287a(20) =21a(21) =37a(22) =881a(23) =2832a(24) =4251a(25) =2832a(26) =881a(27) =37a(28) =65a(29) =2686