a(n) = a(n-1) + a(n-1 minus the number of terms of the same parity as n so far).

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =6a(5) =9a(6) =11a(7) =17a(8) =19a(9) =30a(10) =33a(11) =50a(12) =55a(13) =74a(14) =80a(15) =99a(16) =108a(17) =138a(18) =155a(19) =188a(20) =207a(21) =257a(22) =276a(23) =331a(24) =361a(25) =441a(26) =471a(27) =579a(28) =609a(29) =764