a(n) = Sum_{k = 0..floor(n/2)} floor(C(n-k,k)/(k+1)).

Terms

a(0) =1a(1) =1a(2) =2a(3) =2a(4) =4a(5) =5a(6) =8a(7) =11a(8) =18a(9) =25a(10) =40a(11) =59a(12) =90a(13) =137a(14) =210a(15) =319a(16) =492a(17) =754a(18) =1164a(19) =1798a(20) =2786a(21) =4317a(22) =6710a(23) =10438a(24) =16266a(25) =25377a(26) =39650a(27) =62013a(28) =97108a(29) =152212