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

Author

Clark Kimberling, Aug 19 2011

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A118015.

Programs

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 *)
LinearRecurrence[{1,0,0,0,1,-1},{0,0,1,2,2,2},80] (* Harvey P. Dale, Jun 06 2024 *)

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-1)^2*(1+x+x^2+x^3+x^4)). (End)

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

a(n) = A002266(n+1)+A002266(n+2). - R. J. Mathar, Nov 21 2023