A194228 Partial sums of A194227.

0, 0, 1, 2, 4, 7, 10, 13, 16, 20, 24, 29, 35, 41, 47, 53, 60, 67, 75, 84, 93, 102, 111, 121, 131, 142, 154, 166, 178, 190, 203, 216, 230, 245, 260, 275, 290, 306, 322, 339, 357, 375, 393, 411, 430, 449, 469, 490, 511, 532, 553, 575, 597, 620, 644, 668, 692

Offset

1,4

Links

Table of n, a(n) for n=1..57.

Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 0, 1, -2, 1).

Formula

a(n) = 3/14*n^2 - n/14 + O(1). - 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 *)

Prog

(PARI) a(n)=(3*n^2-n+2*[0, -1, -5, -5, -8, -7, -2][n%7+1])/14 \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Cf. A194227.

Sequence in context: A135678 A001195 A295513 * A194236 A127762 A137281

Adjacent sequences: A194225 A194226 A194227 * A194229 A194230 A194231

Keyword

nonn,easy

Author

Clark Kimberling, Aug 19 2011

Status

approved