a(n) = floor(phi*a(n-1)) + a(n-2) where phi is the golden ratio.

Terms

a(0) =1a(1) =3a(2) =5a(3) =11a(4) =22a(5) =46a(6) =96a(7) =201a(8) =421a(9) =882a(10) =1848a(11) =3872a(12) =8113a(13) =16999a(14) =35617a(15) =74628a(16) =156367a(17) =327635a(18) =686491a(19) =1438400a(20) =3013871a(21) =6314945a(22) =13231666a(23) =27724230a(24) =58090412a(25) =121716491a(26) =255031831a(27) =534366661a(28) =1119655250