a(n) = T(n, floor(n/2)), T given by A026747.

Terms

a(0) =1a(1) =1a(2) =3a(3) =4a(4) =11a(5) =17a(6) =44a(7) =74a(8) =184a(9) =327a(10) =790a(11) =1461a(12) =3452a(13) =6584a(14) =15278a(15) =29879a(16) =68290a(17) =136391a(18) =307696a(19) =625731a(20) =1395696a(21) =2883357a(22) =6367199a(23) =13338421a(24) =29193025a(25) =61920497a(26) =134442102a(27) =288368511a(28) =621609060a(29) =1346873365