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

Terms

a(0) =1a(1) =2a(2) =3a(3) =4a(4) =6a(5) =9a(6) =12a(7) =16a(8) =19a(9) =25a(10) =31a(11) =37a(12) =49a(13) =55a(14) =74a(15) =83a(16) =108a(17) =120a(18) =145a(19) =161a(20) =198a(21) =217a(22) =266a(23) =291a(24) =346a(25) =377a(26) =451a(27) =482a(28) =565a(29) =602