T(n,k)=1/4 the number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having distinct edge sums.

Terms

a(0) =4a(1) =8a(2) =8a(3) =16a(4) =17a(5) =16a(6) =32a(7) =34a(8) =34a(9) =32a(10) =64a(11) =80a(12) =64a(13) =80a(14) =64a(15) =128a(16) =170a(17) =156a(18) =156a(19) =170a(20) =128a(21) =256a(22) =410a(23) =320a(24) =512a(25) =320a(26) =410a(27) =256a(28) =512a(29) =882