a(n) = 2*a(n-1) + (-1)^n*a(floor(n/2)); a(1)=1.

Terms

a(0) =1a(1) =3a(2) =5a(3) =13a(4) =23a(5) =51a(6) =97a(7) =207a(8) =401a(9) =825a(10) =1627a(11) =3305a(12) =6559a(13) =13215a(14) =26333a(15) =52873a(16) =105539a(17) =211479a(18) =422557a(19) =845939a(20) =1691053a(21) =3383733a(22) =6765839a(23) =13534983a(24) =27066661a(25) =54139881a(26) =108273203a(27) =216559621a(28) =433106027a(29) =866238387