T(n,k) = number of 0..k arrays of length n avoiding the consecutive pattern 0..k.

Terms

a(0) =2a(1) =3a(2) =3a(3) =4a(4) =9a(5) =4a(6) =5a(7) =16a(8) =26a(9) =5a(10) =6a(11) =25a(12) =64a(13) =75a(14) =6a(15) =7a(16) =36a(17) =125a(18) =255a(19) =216a(20) =7a(21) =8a(22) =49a(23) =216a(24) =625a(25) =1016a(26) =622a(27) =8a(28) =9a(29) =64