a(n) = 1 + a(floor(n/2))*a(ceiling(n/2)) for n > 1, a(1) = 3.

Terms

a(0) =3a(1) =10a(2) =31a(3) =101a(4) =311a(5) =962a(6) =3132a(7) =10202a(8) =31412a(9) =96722a(10) =299183a(11) =925445a(12) =3012985a(13) =9809425a(14) =31952665a(15) =104080805a(16) =320465225a(17) =986713745a(18) =3038231465a(19) =9355145285a(20) =28937578127a(21) =89510467490a(22) =276877411436a(23) =856448448026