T(n,k)=Number of 0..k arrays of length n+1 with 0 never adjacent to k.

Terms

a(0) =2a(1) =7a(2) =2a(3) =14a(4) =17a(5) =2a(6) =23a(7) =50a(8) =41a(9) =2a(10) =34a(11) =107a(12) =178a(13) =99a(14) =2a(15) =47a(16) =194a(17) =497a(18) =634a(19) =239a(20) =2a(21) =62a(22) =317a(23) =1106a(24) =2309a(25) =2258a(26) =577a(27) =2a(28) =79a(29) =482