a(n)=a(n-1)+a(n-2)-d, where d=a(n/5) if 5 divides n, else d=0; 2 initial terms.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =4a(5) =7a(6) =11a(7) =18a(8) =29a(9) =46a(10) =75a(11) =121a(12) =196a(13) =317a(14) =511a(15) =828a(16) =1339a(17) =2167a(18) =3506a(19) =5670a(20) =9176a(21) =14846a(22) =24022a(23) =38868a(24) =62886a(25) =101754a(26) =164640a(27) =266394a(28) =431034a(29) =697421