a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026758.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =9a(6) =16a(7) =29a(8) =46a(9) =82a(10) =145a(11) =237a(12) =421a(13) =737a(14) =1228a(15) =2171a(16) =3788a(17) =6388a(18) =11253a(19) =19617a(20) =33344a(21) =58597a(22) =102141a(23) =174571a(24) =306294a(25) =533976a(26) =916309a(27) =1605975a(28) =2800260a(29) =4820020