T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock summing to 3 6 or 9.

Terms

a(0) =84a(1) =444a(2) =444a(3) =2356a(4) =3140a(5) =2356a(6) =12556a(7) =22536a(8) =22536a(9) =12556a(10) =67204a(11) =164480a(12) =223164a(13) =164480a(14) =67204a(15) =361244a(16) =1221748a(17) =2302844a(18) =2302844a(19) =1221748a(20) =361244a(21) =1950036a(22) =9240612a(23) =24846540a(24) =34973116a(25) =24846540a(26) =9240612a(27) =1950036a(28) =10570156a(29) =71163896