T(n,k)=Number of nXk 0..3 arrays avoiding the patterns z z+1 z or z z-1 z in any row or column.

Terms

a(0) =4a(1) =16a(2) =16a(3) =58a(4) =256a(5) =58a(6) =214a(7) =3364a(8) =3364a(9) =214a(10) =788a(11) =45796a(12) =147006a(13) =45796a(14) =788a(15) =2902a(16) =620944a(17) =6758694a(18) =6758694a(19) =620944a(20) =2902a(21) =10686a(22) =8421604a(23) =308746116a(24) =1066263778a(25) =308746116a(26) =8421604a(27) =10686a(28) =39350a(29) =114190596