Partial sums are A117451. Second partial sums are A117450.
FORMULA
G.f.: (1-x+x^2+x^5)/(1-x^5)
a(n)=(1/25)*{-9*(n mod 5)+[(n+1) mod 5]+6*[(n+2) mod 5]-9*[(n+3) mod 5]+16*[(n+4) mod 5]}+[(n+2) mod (n+1)]-1, with n>=0. - Paolo P. Lava (ppl(AT)spl.at), Jul 19 2007