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

Terms

a(0) =2a(1) =1a(2) =3a(3) =3a(4) =5a(5) =6a(6) =8a(7) =10a(8) =13a(9) =17a(10) =22a(11) =28a(12) =36a(13) =46a(14) =59a(15) =76a(16) =97a(17) =125a(18) =160a(19) =205a(20) =263a(21) =337a(22) =432a(23) =553a(24) =709a(25) =908a(26) =1163a(27) =1490a(28) =1908a(29) =2444