T(n,k)=1/4 the number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock having distinct edge sums.

Terms

a(0) =22a(1) =124a(2) =124a(3) =696a(4) =1096a(5) =696a(6) =3912a(7) =9712a(8) =9712a(9) =3912a(10) =21976a(11) =86744a(12) =137888a(13) =86744a(14) =21976a(15) =123480a(16) =775096a(17) =1995752a(18) =1995752a(19) =775096a(20) =123480a(21) =693752a(22) =6933120a(23) =28927984a(24) =47572464a(25) =28927984a(26) =6933120a(27) =693752a(28) =3897880a(29) =62007896