A194225 [sum{(k/7) : 1<=k<=n}], where [ ]=floor, ( )=fractional part.

0, 0, 0, 1, 2, 3, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 6, 7, 8, 9, 9, 9, 9, 9, 10, 11, 12, 12, 12, 12, 12, 13, 14, 15, 15, 15, 15, 15, 16, 17, 18, 18, 18, 18, 18, 19, 20, 21, 21, 21, 21, 21, 22, 23, 24, 24, 24, 24, 24, 25, 26, 27, 27, 27, 27, 27, 28, 29, 30, 30, 30, 30, 30, 31

Offset

1,5

Links

Table of n, a(n) for n=1..74.

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

Formula

a(n) ~ 3*n/7. - Charles R Greathouse IV, May 30 2026

Mathematica

r = 1/7;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]    (* A194225 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194226 *)

Prog

(PARI) a(n)=(n-1)\7*3+[3, 0, 0, 0, 1, 2, 3][n%7+1] \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Cf. A194226.

Sequence in context: A200264 A104406 A080344 * A025782 A120506 A327041

Adjacent sequences: A194222 A194223 A194224 * A194226 A194227 A194228

Keyword

nonn,easy

Author

Clark Kimberling, Aug 19 2011

Status

approved