A194227 [sum{(2k/7) : 1<=k<=n}], where [ ]=floor, ( )=fractional part.

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

Offset

1,5

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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 = 2/7;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]    (* A194227 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]   (* A194228 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 1, -1}, {0, 0, 1, 1, 2, 3, 3, 3}, 80] (* Harvey P. Dale, Apr 13 2025 *)

Prog

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

Crossrefs

Cf. A194227.

Sequence in context: A130822 A194220 A189627 * A194819 A194235 A029120

Adjacent sequences: A194224 A194225 A194226 * A194228 A194229 A194230

Keyword

nonn,easy

Author

Clark Kimberling, Aug 19 2011

Status

approved