A194222 a(n) = floor(Sum_{k=1..n} frac(k/5)), where frac() = fractional part.

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

Offset

1,4

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Formula

From Chai Wah Wu, Jun 10 2020: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.

G.f.: x^3*(x + 1)/(x^6 - x^5 - x + 1). (End)

a(n) = floor((n+1)/5) + floor((n+2)/5). - Ridouane Oudra, Dec 14 2021

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

Cf. A118015.

Sequence in context: A261221 A080352 A301426 * A025779 A085003 A119026

Adjacent sequences: A194219 A194220 A194221 * A194223 A194224 A194225

Keyword

nonn,easy

Author

Clark Kimberling, Aug 19 2011

Status

approved