a(n) = Sum_{k=1..n-1}((k mod 5)*a(n-k)), a(1) = 1.

Terms

a(0) =1a(1) =1a(2) =3a(3) =8a(4) =21a(5) =50a(6) =129a(7) =327a(8) =827a(9) =2089a(10) =5290a(11) =13386a(12) =33868a(13) =85693a(14) =216836a(15) =548660a(16) =1388269a(17) =3512737a(18) =8888292a(19) =22490049a(20) =56906580a(21) =143990771a(22) =364339983a(23) =921889753a(24) =2332658401a(25) =5902327520a(26) =14934664284a(27) =37789193522a(28) =95618028007a(29) =241942376384