A194163 a(n) = [sum{(k*r) : 1<=k<=n}], where [ ]=floor, ( )=fractional part, and r=sqrt(3).

0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, 8, 9, 9, 10, 10, 11, 11, 12, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 17, 18, 18, 18, 19, 19, 20, 20, 21, 21, 21, 22, 23, 23, 23, 24, 25, 25, 25, 26, 27, 27, 28, 29, 29, 29, 30, 31, 31, 31, 32, 33, 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. A194164.

Programs

Mathematica

r = Sqrt[3];
a[n_] := Floor[Sum[FractionalPart[k*r], {k, 1, n}]]
Table[a[n], {n, 1, 90}]      (* A194163 *)
s[n_] := Sum[a[k], {k, 1, n}]
Table[s[n], {n, 1, 100}]     (* A194164 *)

PARI

for(n=1,50, print1(floor(sum(k=1,n, frac(k*sqrt(3)))), ", ")) \\ G. C. Greubel, Oct 29 2017