a(n) = Sum_{k=0..floor(n/2)} T(n-k, k), T given by A026692.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =8a(6) =15a(7) =26a(8) =48a(9) =79a(10) =137a(11) =223a(12) =403a(13) =689a(14) =1251a(15) =2088a(16) =3647a(17) =6028a(18) =10775a(19) =18386a(20) =33010a(21) =55460a(22) =96916a(23) =161705a(24) =287199a(25) =490430a(26) =873964a(27) =1475256a(28) =2575673a(29) =4325448