T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to 2 4 or 6.

Terms

a(0) =39a(1) =171a(2) =171a(3) =753a(4) =1115a(5) =753a(6) =3333a(7) =7393a(8) =7393a(9) =3333a(10) =14823a(11) =49937a(12) =75391a(13) =49937a(14) =14823a(15) =66219a(16) =343299a(17) =801579a(18) =801579a(19) =343299a(20) =66219a(21) =297057a(22) =2399159a(23) =8863633a(24) =13857083a(25) =8863633a(26) =2399159a(27) =297057a(28) =1337733a(29) =17016861