a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026736.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =9a(6) =14a(7) =23a(8) =42a(9) =65a(10) =107a(11) =194a(12) =301a(13) =495a(14) =890a(15) =1385a(16) =2275a(17) =4058a(18) =6333a(19) =10391a(20) =18404a(21) =28795a(22) =47199a(23) =83079a(24) =130278a(25) =213357a(26) =373512a(27) =586869a(28) =960381a(29) =1673271