a(1)=1, a(n) = Sum_{k=1..n-1} min(a(k), a(n-k)).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =4a(5) =6a(6) =8a(7) =11a(8) =14a(9) =18a(10) =22a(11) =28a(12) =34a(13) =42a(14) =50a(15) =61a(16) =72a(17) =86a(18) =100a(19) =118a(20) =136a(21) =158a(22) =180a(23) =208a(24) =236a(25) =270a(26) =304a(27) =346a(28) =388a(29) =438