A194169 a(n) = [Sum_{k=1..n} (k*r)], where [ ]=floor, ( )=fractional part, and r=sqrt(5).

0, 0, 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 6, 6, 7, 8, 8, 8, 8, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 17, 17, 18, 19, 19, 20, 21, 21, 21, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 32, 32, 33, 33, 34, 34, 35, 36, 36

Offset: 1

Author

Clark Kimberling, Aug 18 2011

Keywords

• nonn

Links

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

Crossrefs

Cf. A194170.

Programs

Mathematica

r = Sqrt[5];
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]   (* A194169 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]  (* A194170 *)

PARI

a(n) = floor(sum(k=1, n, frac(sqrt(5)*k))); \\ Michel Marcus, Nov 11 2017