T(n,k)=Number of nXk 0..2 arrays with each sum of a(1..i,1..j) no greater than i*j.

Terms

a(0) =2a(1) =5a(2) =5a(3) =13a(4) =34a(5) =13a(6) =35a(7) =249a(8) =249a(9) =35a(10) =96a(11) =1920a(12) =5257a(13) =1920a(14) =96a(15) =267a(16) =15232a(17) =118128a(18) =118128a(19) =15232a(20) =267a(21) =750a(22) =123323a(23) =2748326a(24) =7798591a(25) =2748326a(26) =123323a(27) =750a(28) =2123a(29) =1012996