T(n,k)=Number of nXk arrays of occupancy after each element moves to some king-move neighbor.

Terms

a(0) =0a(1) =1a(2) =1a(3) =2a(4) =31a(5) =2a(6) =4a(7) =318a(8) =318a(9) =4a(10) =8a(11) =3605a(12) =12542a(13) =3605a(14) =8a(15) =16a(16) =39851a(17) =577414a(18) =577414a(19) =39851a(20) =16a(21) =32a(22) =441912a(23) =25530633a(24) =106838218a(25) =25530633a(26) =441912a(27) =32a(28) =64a(29) =4896043