T(n,k)=Number of length n+2 0..k arrays with no consecutive three elements summing to more than k.

Terms

a(0) =4a(1) =10a(2) =6a(3) =20a(4) =20a(5) =9a(6) =35a(7) =50a(8) =40a(9) =13a(10) =56a(11) =105a(12) =125a(13) =76a(14) =19a(15) =84a(16) =196a(17) =315a(18) =295a(19) =147a(20) =28a(21) =120a(22) =336a(23) =686a(24) =889a(25) =711a(26) =287a(27) =41a(28) =165a(29) =540