

A194222


a(n) = floor(Sum_{k=1..n} frac(k/5)), where frac() = fractional part.


2



0, 0, 1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 6, 6, 7, 8, 8, 8, 8, 9, 10, 10, 10, 10, 11, 12, 12, 12, 12, 13, 14, 14, 14, 14, 15, 16, 16, 16, 16, 17, 18, 18, 18, 18, 19, 20, 20, 20, 20, 21, 22, 22, 22, 22, 23, 24, 24, 24, 24, 25, 26, 26, 26, 26, 27, 28, 28, 28, 28, 29, 30
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OFFSET

1,4


LINKS



FORMULA

a(n) = a(n1) + a(n5)  a(n6) for n > 6.
G.f.: x^3*(x + 1)/(x^6  x^5  x + 1). (End)


MAPLE

seq(floor((n+1)/5)+floor((n+2)/5), n=1..80); # Ridouane Oudra, Dec 14 2021


MATHEMATICA

r = 1/5;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}] (* A194222 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}] (* A118015 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



