a(n) = Sum_{i=0..n} T(i,n-i) where T is given by A047020.

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =9a(5) =18a(6) =28a(7) =53a(8) =101a(9) =195a(10) =390a(11) =704a(12) =1371a(13) =2676a(14) =5253a(15) =10506a(16) =19840a(17) =39056a(18) =76968a(19) =152168a(20) =304336a(21) =586864a(22) =1161577a(23) =2300544a(24) =4565558a(25) =9131116a(26) =17813324a(27) =35369544a(28) =70256203a(29) =139745471