T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 2 or 3 king-move neighboring 1s.

Terms

a(0) =1a(1) =2a(2) =2a(3) =4a(4) =12a(5) =4a(6) =7a(7) =43a(8) =43a(9) =7a(10) =12a(11) =145a(12) =210a(13) =145a(14) =12a(15) =21a(16) =524a(17) =1162a(18) =1162a(19) =524a(20) =21a(21) =37a(22) =1888a(23) =6959a(24) =11478a(25) =6959a(26) =1888a(27) =37a(28) =65a(29) =6737