A194223 a(n) = [sum{(k/6) : 1<=k<=n}], where [ ]=floor, ( )=fractional part.

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

Offset

1,5

Links

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

Formula

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

a(n) = a(n-1) + a(n-12) - a(n-13) for n > 13.

G.f.: x*(x^10 + x^9 + x^7 + x^4 + x^2)/(x^13 - x^12 - x + 1). (End)

Mathematica

r = 1/6;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]    (* A194223 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194224 *)

Prog

(PARI) for(n=1, 50, print1(floor(sum(k=1, n, frac(k/6))), ", ")) \\ G. C. Greubel, Oct 29 2017

Crossrefs

Cf. A194224.

Sequence in context: A239913 A323701 A226591 * A371587 A194251 A029114

Adjacent sequences: A194220 A194221 A194222 * A194224 A194225 A194226

Keyword

nonn

Author

Clark Kimberling, Aug 19 2011

Status

approved