T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1s.

Terms

a(0) =1a(1) =2a(2) =2a(3) =3a(4) =8a(5) =3a(6) =4a(7) =16a(8) =16a(9) =4a(10) =6a(11) =36a(12) =45a(13) =36a(14) =6a(15) =9a(16) =112a(17) =135a(18) =135a(19) =112a(20) =9a(21) =13a(22) =256a(23) =544a(24) =620a(25) =544a(26) =256a(27) =13a(28) =19a(29) =608