a(n) = Sum_{k=0..floor(n/2)} A000108(n-k).

Terms

a(0) =1a(1) =1a(2) =3a(3) =7a(4) =21a(5) =61a(6) =193a(7) =617a(8) =2047a(9) =6895a(10) =23691a(11) =82435a(12) =290447a(13) =1033215a(14) =3707655a(15) =13402071a(16) =48759741a(17) =178403101a(18) =656041801a(19) =2423300129a(20) =8987420549a(21) =33453670773a(22) =124936234413a(23) =467995789277