T(n,k) is the number of arrays of n+2 elements from {0,1,...,k} with no two consecutive ascents.

Terms

a(0) =8a(1) =26a(2) =16a(3) =60a(4) =75a(5) =32a(6) =115a(7) =225a(8) =216a(9) =64a(10) =196a(11) =530a(12) =840a(13) =622a(14) =128a(15) =308a(16) =1071a(17) =2425a(18) =3136a(19) =1791a(20) =256a(21) =456a(22) =1946a(23) =5796a(24) =11100a(25) =11704a(26) =5157a(27) =512a(28) =645a(29) =3270