a(1)=a(2)=1, a(n)=a(n-1)+a(n-2) if n is odd, a(n)=a(n-1)+a(n/2) if n is even.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =5a(5) =7a(6) =12a(7) =15a(8) =27a(9) =32a(10) =59a(11) =66a(12) =125a(13) =137a(14) =262a(15) =277a(16) =539a(17) =566a(18) =1105a(19) =1137a(20) =2242a(21) =2301a(22) =4543a(23) =4609a(24) =9152a(25) =9277a(26) =18429a(27) =18566a(28) =36995a(29) =37257