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

Terms

a(0) =19a(1) =45a(2) =45a(3) =115a(4) =87a(5) =115a(6) =309a(7) =189a(8) =189a(9) =309a(10) =859a(11) =447a(12) =355a(13) =447a(14) =859a(15) =2445a(16) =1125a(17) =741a(18) =741a(19) =1125a(20) =2445a(21) =7075a(22) =2967a(23) =1675a(24) =1383a(25) =1675a(26) =2967a(27) =7075a(28) =20709a(29) =8109