T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to 3 4 or 5.

Terms

a(0) =51a(1) =309a(2) =309a(3) =1899a(4) =3921a(5) =1899a(6) =11709a(7) =50831a(8) =50831a(9) =11709a(10) =72243a(11) =663307a(12) =1401453a(13) =663307a(14) =72243a(15) =445797a(16) =8671957a(17) =39019417a(18) =39019417a(19) =8671957a(20) =445797a(21) =2751003a(22) =113445117a(23) =1089569635a(24) =2324761359a(25) =1089569635a(26) =113445117a(27) =2751003a(28) =16976493