a(0)=0, a(1)=1, a(n)=a(n-1)+a(n-2)+a(n-3) if a(n-1) is even, a(n)=a(n-1)+a(n-2) if a(n-1) is odd.

Terms

a(0) =0a(1) =1a(2) =1a(3) =2a(4) =4a(5) =7a(6) =11a(7) =18a(8) =36a(9) =65a(10) =101a(11) =166a(12) =332a(13) =599a(14) =931a(15) =1530a(16) =3060a(17) =5521a(18) =8581a(19) =14102a(20) =28204a(21) =50887a(22) =79091a(23) =129978a(24) =259956a(25) =469025a(26) =728981a(27) =1198006a(28) =2396012a(29) =4322999