Euler transform of 2^floor(n/2), (A016116).

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =12a(5) =20a(6) =43a(7) =73a(8) =146a(9) =250a(10) =475a(11) =813a(12) =1499a(13) =2555a(14) =4592a(15) =7800a(16) =13761a(17) =23253a(18) =40421a(19) =67963a(20) =116723a(21) =195291a(22) =332026a(23) =552882a(24) =932023a(25) =1544943a(26) =2585243a(27) =4267081a(28) =7094593a(29) =11662769