A194166 Partial sums of A194165.

0, 0, 1, 3, 5, 7, 10, 14, 18, 22, 27, 33, 39, 45, 52, 60, 68, 76, 85, 94, 104, 115, 126, 138, 150, 162, 175, 188, 202, 217, 232, 248, 264, 280, 297, 314, 332, 350, 369, 388, 408, 429, 450, 471, 493, 516, 539, 562, 586, 610, 635, 660, 686, 712, 739, 767

Offset: 1

Author

Clark Kimberling, Aug 18 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A194165.

Programs

Mathematica

r = GoldenRatio;
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]   (* A194165 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]  (* A194166 *)